Fanny Lalloyer

Kristiaan Wouters

Morgane Baron

Sandrine Caron

Emmanuelle Vallez

Jonathan Vanhoutte

Eric Baugé

Ronit Shiri-Sverdlov

Hofker Marten

Bart Staels
email: <bart.staels@pasteur-lille.fr

Eric Baug

Anne Tailleux

R Cepteurs Nucl Aires

Maladies Cardiovasculaires

Peroxisome proliferator-activated receptor-alpha gene level differently affects lipid metabolism and inflammation in apolipoprotein

Keywords: Analysis of Variance, Animals, Anti-Inflammatory Agents, pharmacology, Aorta, drug effects, metabolism, pathology, Apolipoprotein E2, genetics, metabolism, Atherosclerosis, drug therapy, genetics, metabolism, pathology, Disease Models, Animal, Fatty Liver, drug therapy, genetics, metabolism, pathology, Female, Fenofibrate, pharmacology, Gene Expression Regulation, Gene Knock-In Techniques, Heterozygote, Homozygote, Humans, Hypolipidemic Agents, pharmacology, Inflammation, drug therapy, genetics, metabolism, pathology, Lipid Metabolism, drug effects, genetics, Lipids, blood, Liver, drug effects, metabolism, pathology, Mice, Mice, Inbred C57BL, Mice, Knockout, Mice, Transgenic, PPAR alpha, agonists, genetics, metabolism PPARalpha, fatty liver disease, atherosclerosis, inflammation, lipid metabolism, murine model

Introduction

Fibrates are lipid-lowering drugs widely used in clinical practice to treat dyslipidemia . Studies performed in Peroxisome [START_REF] Staels | Fibrates and future PPARalpha agonists in the treatment of cardiovascular disease[END_REF] Proliferator-Activated Receptor (PPAR )-deficient mice have demonstrated that the hypolipidemic effects of fibrates are due to α α activation of PPAR , a ligand-activated transcription factor which modulates lipid metabolism . PPAR is expressed in many tissues, α [START_REF] Peters | Alterations in lipoprotein metabolism in peroxisome proliferator-activated receptor alpha-deficient mice[END_REF] α particularly in tissues with high fatty acid oxidation rates such as liver, kidney, heart and muscle. After activation by fibrates, PPAR binds α as a heterodimer with the Retinoid X Receptor (RXR) to PPAR response elements (PPRE) in the promoters of genes implicated in lipid and lipoprotein metabolism. In addition to its effects on lipid metabolism, PPAR also inhibits pro-inflammatory pathways by negatively α interfering with other signalling pathways such as NF-kB, STATs (Signal Transducer and Activator of Transcription) or AP-1 (Activator Protein-1). Consequently, through its effects on lipid metabolism and inflammation, PPAR may modulate pathophysiological pathways α implicated in fatty liver disease and atherosclerosis. Data concerning the implication of PPAR in liver steatosis and inflammation in α humans is scarce. However, it has been shown that PPAR agonist treatment decreases non-alcoholic steatohepatitis (NASH) development α in wild-type mice fed a methionine choline-deficient (MCD) diet , and apoE2 knock-in (apoE2-KI) mice or foz/foz mice fed a [3 4 ] high-fat diet , . Moreover, PPAR is expressed in many cell types found in the atherosclerotic lesion such as macrophages, [5 6 ] α endothelial cells and smooth muscle cells (SMC) . I and studies have suggested that fibrates could exert anti-atherogenic [START_REF] Lefebvre | Sorting out the roles of PPAR alpha in energy metabolism and vascular homeostasis[END_REF] n vitro in vivo actions by improving lipid abnormalities and/or by modulating several steps of atherogenesis such as decreasing inflammation and thrombosis directly in the vascular wall. In humans, fibrates decrease cardiovascular disease especially in patients with high triglyceride (TG) and low high density lipoprotein-cholesterol (HDL-C) levels . Moreover, we have previously shown that fenofibrate treatment [START_REF] Staels | Fibrates and future PPARalpha agonists in the treatment of cardiovascular disease[END_REF] reduces macrophage-laden atherosclerotic lesions in apoE2-KI mice, a mouse model of NASH, atherosclerosis and mixed dyslipidemia [START_REF] Hennuyer | PPARalpha, but not PPARgamma, activators decrease macrophage-laden atherosclerotic lesions in a nondiabetic mouse model of mixed dyslipidemia[END_REF] . However, the role of PPAR in atherosclerosis is controversial, since PPAR -deficiency protects against atherosclerosis progression in In the present study, we aimed to analyze the consequences of PPAR -deficiency on lipid metabolism and inflammation in the α vascular wall and the liver using apoE2-KI mice, a model of mixed dyslipidemia, atherosclerosis and NASH, and to further explore the implication of PPAR in the response to fenofibrate treatment. Therefore, wildtype ( / ), heterozygous ( / ) and homozygous PPAR

Materials and Methods

Animals

Homozygous PPAR -deficient mice on the C57BL/6 background were crossed with homozygous human apoE2-KI mice ,

α [15 ] [16 ]
which express human apoE2 instead of mouse under control of the endogenous promoter, to generate PPAR / , PPAR / and apoe

Plasma lipid and lipoprotein analyses

Mice were fasted for 4 hours before retro-orbital puncture under isoflurane-induced anesthesia. Plasma concentrations of total cholesterol (TC) and triglycerides (TG) were measured using commercially available kits (Biomerieux, France).

Hepatic lipid analysis

Frozen liver tissue (50 mg) was homogenized in SET buffer (1 mL; sucrose 250 mM, EDTA 2 mM and Tris 10 mM), followed by two freeze-thaw cycles and three times passing through a 27-gauge syringe needle and a final freeze-thaw cycle to ensure complete cell lysis.

Protein content was determined with the BCA method and TG and cholesterol was measured as described above.

Liver immunohistochemistry

7 m frozen-cut liver sections were fixed in acetone and stained with Mac1 (M1/70) antibodies, as described .

μ [5 ]

Isolation of primary hepatocytes

Primary hepatocytes were isolated from the livers of fed mice, as previously described .

[17 ]

RNA extraction and quantitative PCR analysis

RNA, isolated from livers using the acid guanidinium thiocyanate/phenol/chloroform method , was reverse transcribed using [START_REF] Chomczynski | Single-step method of RNA isolation by acid guanidinium thiocyanate-phenol-chloroform extraction[END_REF] random hexamer primers and Moloney murine leukemia virus-reverse transcriptase (Invitrogen, France). RNA levels were determined by real-time quantitative PCR on a MX-4000 apparatus (Stratagene) using the Brilliant SYBR Green QPCR master mix (Stratagene) and specific primers. Results are expressed normalized to cyclophilin.

Atherosclerotic lesion analysis

At the end of the diet, mice were euthanized, the hearts were perfused with cold Krebs-Ringer buffer and fixed in a solution containing 4 phosphate-buffered paraformaldehyde. Serial 10 m-thick cryosections were cut between the valves and the aortic arch and % μ atherosclerotic lesions were quantified by Oil-Red-O staining. Images were captured using a JVC 3-CCD video camera and analyzed using the computer-assisted Quips Image analysis system (Leica Mikroskopic und System GmbH, Germany). Cryosections from aortic lesions were stained with anti-mouse MOMA-2 (Santa Cruz Biotechnology) or anti-mouse MCP-1 (Santa Cruz Biotechnology). MCP-1 protein levels were semi-quantitatively scored for staining on lesions of 4 mice per group.

Statistical analysis

Results are expressed as the means SE. Data were compared by ANOVA. Significant differences were subjected to post-hoc analysis ± by using the Scheffe-test. A value of p<0.05 was considered as statistically significant.

Results

Homozygous PPAR -deficiency does not modify plasma lipid concentrations, but aggravates liver steatosis and inflammation in α apoE2-KI mice fed a western diet Female PPAR / , PPAR / and PPAR / apoE2-KI mice were generated and PPAR mRNA levels were found to be

α+ + α+ - α-- α
respectively intermediate and undetectable in the livers of PPAR / and PPAR / vs PPAR / apoE2-KI mice (

α+ - α-- α+ + supplemental figure
). These mice were fed a western diet which was previously shown to induce liver steatosis and inflammation . After 9 weeks of 1A [START_REF] Shiri-Sverdlov | Early diet-induced non-alcoholic steatohepatitis in APOE2 knock-in mice and its prevention by fibrates[END_REF] western diet feeding, plasma TG and TC concentrations were similar in the three groups of mice (

). Relative liver weight figure 1,A B was not different between the three genotypes (

) and liver cholesterol content was slightly, but not significantly supplemental figure 1B increased in PPAR / apoE2-KI compared to PPAR / and PPAR / apoE2-KI mice (

). PPAR / apoE2-KI

α-- α+ + α+ - supplemental figure 1C α--
mice displayed more severe steatohepatitis, as illustrated by higher levels of liver TG ( ) and increased numbers of Mac1-positive figure 1C cells ( ), compared to PPAR / mice. Interestingly, heterozygous PPAR / apoE2-KI mice displayed a similar phenotype as figure 1D α+ + α+ -PPAR / mice ( ). These results demonstrate that PPAR -deficiency does not modify plasma lipid concentrations, and only

α+ + figure 1, C D - α
homozygous PPAR -deficiency aggravates liver steatosis and macrophage content in western diet-fed apoE2-KI mice.

α PPAR activation improves plasma and hepatic lipid homeostasis in PPAR / and PPAR / , but not PPAR / apoE2-KI mice

α α+ + α+ - α--

fed a western diet

To determine the role of the PPAR gene level on the hepatic and plasma response to its agonist fenofibrate, female PPAR / , PPAR PPAR is a transcription factor which regulates the expression of genes involved in fatty acid uptake and oxidation in parenchymal cells of α the liver, mRNA levels for fatty acid translocase (FAT), very long chain acyl-CoA dehydrogenase (VLCAD), long chain acyl-CoA dehydrogenase (LCAD) and medium chain acyl-CoA dehydrogenase (MCAD) were measured ( ). Fenofibrate increased the figure 3,A D hepatic expression levels of all these genes in PPAR / but not in PPAR / apoE2-KI mice. However, in PPAR / apoE2-KI mice,

α+ + α-- α+ -
the expression of these genes increased to a similar extent as in PPAR / apoE2-KI mice upon fenofibrate treatment. A comparable α+ + induction of genes implicated in hepatic lipid metabolism was also observed in primary hepatocytes isolated from PPAR / and PPAR α+ + α+ / apoE2-KI mice and treated with the specific PPAR agonist, GW647, whereas this induction was not observed in PPAR / apoE2-KI

- α α--

hepatocytes (

). Thus, only one allele of the PPAR gene is required for an optimal response to fenofibrate on supplemental figure 2,A

Discussion

Using apoE2-KI mice, a humanized mouse model of mixed dyslipidemia and NASH , we show that homozygous PPAR [START_REF] Sullivan | Type III hyperlipoproteinemia and spontaneous atherosclerosis in mice resulting from gene replacement of mouse Apoe with human Apoe 2 *[END_REF] α

-deficiency aggravates western diet-induced steatosis and inflammation in the liver. This result is consistent with the reported increased hepatic steatosis observed in PPAR -deficient mice in response to the physiological stimulus fasting , further illustrating the role α [20 ]- [START_REF] Hashimoto | Defect in peroxisome proliferator-activated receptor alpha-inducible fatty acid oxidation determines the severity of hepatic steatosis in response to fasting[END_REF] of PPAR in hepatic lipid metabolism. In apoE2-KI mice, aggravation of NASH induced by PPAR -deficiency was not accompanied by α α changes of plasma TC and TG concentrations nor atherosclerosis lesion development, suggesting a dissociation between both pathological states. We also analyzed the effects of PPAR gene level on the response to treatment with the PPAR agonist fenofibrate on NASH.

α α

Fenofibrate treatment protected against NASH in western diet-fed PPAR / but not PPAR / apoE2-KI mice, showing that the

α+ + α--
previously reported effects of fenofibrate on NASH in apoE2-KI mice occur via PPAR . Interestingly, fenofibrate treatment of PPAR [START_REF] Shiri-Sverdlov | Early diet-induced non-alcoholic steatohepatitis in APOE2 knock-in mice and its prevention by fibrates[END_REF] α α / apoE2-KI mice resulted in decreased hepatic steatosis to an extent similar as PPAR / apoE2-KI mice. In parallel, the hepatic

+ - α+ +
expression of genes implicated in fatty acid uptake and oxidation increased to a similar extent in fenofibrate-treated PPAR / and PPAR α+ -α / apoE2-KI mice. However, in contrast with the regulation of lipid metabolism, the anti-inflammatory response to fenofibrate in the liver with fenofibrate improves metabolic syndrome parameters, including the lipid profile, and has beneficial effects on certain liver function parameters, but its impact on liver histology was small . Another study has suggested a beneficial effect of fenofibrate treatment, [START_REF] Fernandez-Miranda | A pilot trial of fenofibrate for the treatment of non-alcoholic fatty liver disease[END_REF] particularly in combination with statins, in reducing fatty liver disease . Further studies are needed to evaluate the impact of PPAR [START_REF] Athyros | Effect of multifactorial treatment on non-alcoholic fatty liver disease in metabolic syndrome: a randomised study[END_REF] α agonists on NAFLD, and in particular on the inflammatory component of NASH.

We show that PPAR is required for the fenofibrate-induced improvement of dyslipidemia in apoE2-KI mice and a single PPAR

α α
allele is sufficient to mediate this effect, showing that PPAR gene level does not determine the plasma lipid-response of fenofibrate. In α the Lower Extremity Arterial Disease Event Reduction (LEADER) trial, PPAR gene variation did not influence the magnitude of plasma α TG lowering in response to bezafibrate, whereas genetic variation in the PPAR gene affected the changes in plasma fibrinogen, an α inflammatory response marker, to fibrate treatment . Together with our data, variation in PPAR gene activity or expression level [START_REF] Pineda Torra | Characterization of the human PPARalpha promoter: identification of a functional nuclear receptor response element[END_REF] α appears of lesser impact on the lipid response to fibrate, but of higher impact on the inflammatory response.

Since growing evidence links fatty liver disease to cardiovascular disease and since apoE2-KI mice develop dyslipidemia and [START_REF] Targher | Risk of cardiovascular disease in patients with nonalcoholic fatty liver disease[END_REF] NASH as well as atherosclerosis, we also assessed the role of PPAR on vascular inflammation and atherosclerosis. Interestingly, despite α the more severe NASH progression, PPAR / , PPAR / and PPAR / apoE2-KI mice developed quantitatively similar α+ + α+ -α-atherosclerotic lesion areas (as assessed by lipid, macrophage and MCP-1 content of the atherosclerotic plaques), indicating that PPARα does not modulate atherogenesis and vascular inflammation in apoE2-KI mice. This result is surprising since a study performed in LDLR-deficient mice demonstrated that macrophage PPAR confers anti-atherogenic effects via modulation of macrophage cholesterol α trafficking and inflammatory activity . Similar as in apoE2-KI mice, plasma lipid concentrations were not modified by PPAR [START_REF] Babaev | Macrophage expression of peroxisome proliferator-activated receptor-alpha reduces atherosclerosis in low-density lipoprotein receptor-deficient mice[END_REF] α

-deficiency in these LDLR-deficient mice, indicating that differences in plasma lipids do not explain the observed discrepancies of lesion formation between both models. The lesions in apoE2-KI mice mainly consist of foam cells, as occurs in the initial stages of atherogenesis in humans, whereas LDLR-deficient mice develop more advanced atherosclerotic plaques . Thus, the PPAR gene may not modulate [START_REF] Wouters | Understanding hyperlipidemia and atherosclerosis: lessons from genetically modified apoe and ldlr mice[END_REF] α the first stages of lesion formation, but could influence the progression of atherosclerosis to more complex stages. Surprisingly, PPARα -deficiency in apoE-deficient mice, another mouse model of atherosclerosis characterized by a wide spectrum of lesions going from fatty streaks to fibro-proliferative lesions , resulted in a protection against atherosclerotic lesion formation upon western diet feeding, [START_REF] Zhang | Diet-induced atherosclerosis in mice heterozygous and homozygous for apolipoprotein E gene disruption[END_REF] notwithstanding a pro-atherogenic lipid profile characterized by higher levels of TG and TC . However, in contrast to apoE2-KI mice, [START_REF] Tordjman | PPARalpha deficiency reduces insulin resistance and atherosclerosis in apoE-null mice[END_REF] apoE-deficient mice do not respond to PPAR agonists as humans, displaying no change or an increase in plasma lipids upon activation, in addition to being determined by the plasma lipid concentrations, also depends on other parameters, such as inflammation in the artery wall and the liver.

The pathophysiological role of PPAR in atherosclerosis has been investigated using two different and complementary strategies: , it has been shown that [START_REF] Pineda Torra | Characterization of the human PPARalpha promoter: identification of a functional nuclear receptor response element[END_REF] In vitro the V162 variant displays higher PPRE-dependent transcriptional activity , , whereas the intron 7 C allele was hypothesized to be [ [START_REF] Flavell | Variation in the PPARalpha gene is associated with altered function in vitro and plasma lipid concentrations in Type II diabetic subjects[END_REF] Footnotes:

  -KI mice. Three month-old female mice of the three genotypes (n 11 per group) were fed a Western diet containing 0.2 α--= cholesterol and 21 fat (wt/wt) (UAR, France) without (control group, CON) or with fenofibrate (FF) for 9 weeks. Based on food % % consumption, the dose of fenofibrate corresponded to ~100 mg/kg of body weight. Mice were maintained under a 12 hour light/dark cycle and had free access to water. All animal experiments were conducted with the approval of the Pasteur Institute review board, Lille, France.

α

  genetic deficiency and a pharmacological intervention. PPAR -deficiency did not result in the opposite phenotype of fenofibrate-induced α activation of PPAR on atherosclerotic lesion areas. It is well established that nuclear-receptor deficiency does not always mirror α ligand-activation, which may be due to possible compensation mechanisms and/or the absence of active repression of target genes by the unliganded nuclear receptor via co-repressor recruitment. However, the effects of fenofibrate did require PPAR expression, since it was α absent in PPAR / apoE2-KI mice.α--In the Lopid Coronary Angiography Trial (LOCAT) study, the PPAR V162 allele was associated with reduced progression of α atherosclerosis, whereas the intron C allele was associated with greater progression of atherosclerosis .

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5

 12345 Figure 1 Homozygous PPAR -deficiency does not modify plasma lipid concentrations, but aggravates liver steatosis and inflammation in apoE2-KI α mice Blood samples were collected after a 4-hour fast for measurements of plasma TC ( ) and TG ( ) levels in female PPAR / , PPAR / A B α+ + α+ -and PPAR / apoE2-KI mice fed a western diet for 9 weeks. Liver TG content ( ) and MAC-1 staining ( ) were quantified in the liver. n α--

PPAR gene levels do not influence atherogenesis, but determine the atheroprotective response to fenofibrate in apoE2-KI mice

  B By contrast, fenofibrate did not influence the expression of these inflammatory markers in α+ + livers of PPAR / apoE2-KI mice. Interestingly, fenofibrate-treated PPAR / apoE2-KI mice exhibited an intermediary gene inhibition of the hepatic inflammatory response by fenofibrate in apoE2-KI mice fed a western diet.Since non-alcoholic fatty liver disease is now considered a risk factor for cardiovascular disease , atherogenesis and vascular[START_REF] Targher | Risk of cardiovascular disease in patients with nonalcoholic fatty liver disease[END_REF] inflammation were assessed in PPAR / , PPAR / and PPAR / apoE2-KI mice fed a western diet supplemented or not with fenofibrate. Interestingly, the mean aortic lesion area, as measured by lipid staining with oil-red-O, did not differ significantly between

	response was seen in PPAR / apoE2-KI cells ( α+ -	supplemental figure 2, C D -	). Thus, both PPAR alleles are necessary for an optimal α
			α+ +	α+ -	α--
	PPAR / , PPAR / and PPAR / apoE2-KI mice ( α+ + α+ -α--	figure 5, A B -	). As expected	[8 ]	, mean lesion area was significantly reduced by
	about 80 in fenofibrate-treated PPAR / mice compared to controls (median: 0.030 mm in treated mice vs 0.166 mm in control mice, % α+ + 2 2
	p<0.001) (	figure 5, A B -	). By contrast, no effect was observed in fenofibrate-treated PPAR / apoE2-KI mice (median: 0.137 mm in α--2
	treated mice vs 0.123 mm in control mice, NS). Interestingly, treatment of PPAR / apoE2-KI mice with fenofibrate resulted in a 2 α+ -
	significant, intermediary decrease in atherosclerotic lesion area (median: 0.138 mm in treated mice vs 0.185 in control mice, p<0.05), 2
	indicating a dose-response effect of PPAR gene expression on arterial wall lipid accumulation. To determine whether the modifications in α
	atherosclerotic lipid accumulation were associated with altered inflammation in the arterial wall, immunostaining for MOMA-2 (specific
	of macrophages) and MCP-1 was performed in the lesions. Both MOMA-2 (	figure 5C	) and MCP-1(	figure 5, D E -	) co-localized with
	oil-red-O staining, were intense and did not differ between PPAR / , PPAR / and PPAR / apoE2-KI mice, in accordance with the α+ + α+ -α--
	comparable lesion areas between the three genotypes (	figure 5A	). Treatment with fenofibrate strongly decreased MOMA-2 and MCP-1
	staining in the lesions of PPAR / but not PPAR / apoE2-KI mice, indicating PPAR -dependency. Interestingly, fenofibrate treatment α+ + α--α
			-			α
	dyslipidemia and liver steatosis.
	PPAR activation decreases hepatic inflammation and macrophage content in PPAR / , but not PPAR / and PPAR / α α+ + α+ -α--
	apoE2-KI mice fed a western diet
	Hepatic inflammation was analysed in the fenofibrate-treated mice. Fenofibrate treatment decreased the number of Mac-1 positive
						α+ +	α+ -	α--	figure 4, A B
		α--				α+ -
	α					α+ +

cells, indicative of the number of macrophages, in livers of PPAR / but not PPAR / or PPAR / apoE2-KI mice (

).

-

The expression of monocyte chemoattractant protein-1 (MCP-1), intercellular adhesion molecule-1 (ICAM-1) and vascular cell adhesion molecule-1 (VCAM-1), which are implicated in monocyte/macrophage recruitment in the liver ( ), were decreased in figure

4

, C E fenofibrate-treated PPAR / apoE2-KI mice. expression level of MCP-1, VCAM-1 and ICAM-1. Of note, repression of LPS-induced MCP-1 and VCAM-1 expression by the specific PPAR agonist GW647 was most pronounced in isolated primary hepatocytes from PPAR / apoE2-KI mice, whereas an intermediary α fed a western diet of PPAR / apoE2-KI mice resulted in an intermediary phenotype with a slight decrease of MOMA-2 and MCP-1 staining in the lesions. α+ -Thus, while PPAR gene levels do not influence atherosclerosis development, they determine the response to fenofibrate on both lipid α deposition and inflammation in the arterial wall of apoE2-KI mice.

  Until now, no null mutations of PPAR have been identified in humans, but the hepatic PPAR expression levels vary largely among

			α+ -
	with the specific PPAR agonist GW647. Thus, PPAR gene level differently influences fenofibrate s effects on hepatic steatosis and α α '
	inflammation. A single PPAR allele is sufficient for an optimal response of lipid metabolism to fenofibrate, whereas both alleles are
			α			α
	individuals	[23 ]	and several PPAR mutations have been reported α	, [24 25 ]	. Presently, the implication of PPAR in fatty liver disease and α
	a possible modulation by PPAR agonists is still unclear. Magnetic Resonance Imaging (MRI) analysis of liver fat in fifteen type 2 α
	diabetic patients has failed to show any changes in response to fenofibrate	[26 ]	. A pilot study in NAFLD patients has shown that treatment

+ +

depends on both PPAR alleles. Indeed, fenofibrate treatment strongly reduced inflammation and macrophage content in livers of PPAR α α+ / apoE2-KI mice (associated with decreased expression levels of MCP-1, ICAM-1, VCAM-1), whereas little or no response to fenofibrate + was observed in livers of PPAR / apoE2-KI mice. Similar observations were made in isolated heterozygous primary hepatocytes treated α required to obtain maximal anti-inflammatory effects in the liver.

  fibrate treatment, and may therefore not be a suitable model to study the impact of PPAR agonists and possibly other lipid-lowering drugs PPAR activation with fenofibrate protected western diet-fed PPAR / but not PPAR / apoE2-KI mice against atherosclerosis in an intermediary level of atheroprotection and vascular anti-inflammatory response (assessed by MOMA-2 and MCP-1 staining). Thus, the PPAR gene level dose-dependently controls the response to its agonist on vascular inflammation and atherogenesis, despite a similar α plasma lipid response in PPAR / and PPAR / apoE2-KI mice. These observations suggest that atheroprotection upon PPAR

			α	[13 ]	[12 ]
				α
	on atherosclerosis	, [30 32 ]	.
	α			α+ +	α--
	progression, showing PPAR -dependency of the response to fenofibrate. Treatment of PPAR / apoE2-KI mice with fenofibrate resulted α α+ -
			α+ +	α+ -	α

  33 ] associated with lower expression levels of PPAR . Collectively, these results suggest that variations in PPAR gene level or activity

	α [29 ]		α
	are associated with differential progression of atherosclerosis in humans. Both PPAR variants did not influence plasma lipid
	α		α
	modulate the different activities of PPAR (SPPARM effect) α	[34 ]	, the effects of PPAR variants on the response to its agonists could be α
	different according to the PPAR agonist used. Thus, it will be of interest to study the impact of PPAR variants on the responses to α α
	different agonists on fatty liver disease and to assess the association of modifications of lipid metabolism and inflammatory parameters
	with PPAR polymorphisms.

α concentrations in either study, suggesting that, in line with our results, PPAR gene variation may influence atherosclerosis via α mechanisms complementary to the PPAR regulation of plasma lipid concentrations. Finally, since PPAR agonists may selectively α Acknowledgements: Sources of funding This work was supported by grants of ACI 02 20475 (French Research Ministery and Servier laboratory), Veni: 916.76.070 (2006/00496/MW); Maag Lever Darm Stichting (MLDS) (WO 08-16), the foundation Coeur et Art res, the EU grant Hepadip 018734, R è é gion Nord-Pas de Calais/FEDER, and a Kootstra fellowship from Maastricht University.

Disclosure None


E Darles

B Crespin

D Ghazanfarpour

J C Gonzato

A survey of ocean simulation and rendering techniques in computer graphics

Keywords: Descriptors (according to ACM CCS): I, 3, 7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Animation I, 3, 8 [Computer Graphics]: Applications-

This paper presents a survey of ocean simulation and rendering methods in computer graphics. To model and animate the ocean's surface, these methods mainly rely on two main approaches: on the one hand, those which approximate ocean dynamics with parametric, spectral or hybrid models and use empirical laws from oceanographic research. We will see that this type of methods essentially allows the simulation of ocean scenes in the deep water domain, without breaking waves. On the other hand, physically-based methods use Navier-Stokes Equations (NSE) to represent breaking waves and more generally ocean surface near the shore. We also describe ocean rendering methods in computer graphics, with a special interest in the simulation of phenomena such as foam and spray, and light's interaction with the ocean surface.

Introduction

The main goal of computer graphics is to reproduce in the most true-to-life possible way the perceived reality with all the complexity of natural phenomena surrounding us. The ocean's complexity is mainly due to a highly dynamic behavior. Ranging from a quiet sea to an agitated ocean, from small turbulent waves to enormous shorebreaks, the dynamic motion of the ocean is influenced by multiple phenomena occurring at small and large scales. For several centuries, scientists have tried to understand and explain these mechanisms. In oceanographic research, physicists define the behavior of the ocean surface depending on its location: in deep ocean water areas (far from the coast), intermediate areas or shallow water areas (close to the shore). This classification characterizes wave motions with different parameters. In deep waters, the free surface defined by the interface between air and water is generally subjected to a large oscillatory behavior, whereas in shallow waters waves break near the shore. Representing the visual complexity of these phenomena is a challenge, and the last 30 years have seen computer graphics evolve in order to address this issue.

Different models can be used to represent ocean dynamics: parametric description, spectral description as well as models from Computational Fluid Dynamics (CFD) and more specifically Navier-Stokes Equations (NSE). The first category aims at computing the path of water particles and describes the free surface with parametric equations based on real observations, obtained from buoys or satellite measurements [START_REF] Biesel | Study of wave propagation in water of gradually varying depth[END_REF]. The second category approximates the state of the sea by using waves spectrum [PM64, HBB * 73, BGRV85] and computes waves distribution according to their amplitudes and frequencies. Finally, NSE can represent dynamics of all types of fluid, including the dynamical behavior of the ocean.

Ocean simulation methods in the computer graphics domain can therefore be classified into two main categories: parametric/spectral methods that use oceanographic models, and physically-based methods relying on NSE. Parametric/spectral models work best in deep waters where they accurately represent the periodical motion of the sea. But since they do not take into account the interactions with the bottom of the sea in shallow waters, only physically-based methods deriving approximate solutions from NSE can reproduce the complexity of ocean dynamics near the shore.

Another important characteristics of oceans for computer graphics is their complex optical properties. For example, the color of ocean waters, varying from green to deep blue, is related to the concentration of phytoplankton particles. Several other phenomena, such as foam, sprays, water properties (turbidity, bubbles, . . . ) and light-water exchanges must also be simulated at the rendering stage. Addressing the simulation of these phenomena is a precondition to obtain realistic ocean scenes. This paper presents a survey of research works in ocean simulation and rendering in computer graphics. This includes different methods specifically designed for ocean scenes, but also more general water simulation techniques that can be applied to ocean simulation. Papers presenting specific methods for fluid simulation, intended for example for rivers [START_REF] Thon | A semi-physical model of running waters[END_REF]YNBH09] or fountains [WCHJ06] are not covered here; interested readers can also refer to [START_REF] Iglesias | Computer graphics for water modeling and rendering: a survey[END_REF] where a more general survey of water simulation techniques is presented.

In sections 2 and 3, we will focus on the methods specifically intended to model and animate the detailed surface of the ocean. We will use the classification presented in the previous paragraph: parametric/spectral methods describing the surface using models from oceanography, and NSEbased methods that simulate the dynamic behaviour of ocean waves. Section 4 is dedicated to realistic ocean rendering, particularly the representation of foam and sprays and the simulation of different light-water interactions. Finally, we will conclude by presenting possible perspectives for these techniques.

Ocean dynamics simulation in deep water

The methods presented in this section use theoretical models and/or experimental observations to describe the ocean surface in deep water and represent swell effects. We can subdivide these methods into three main categories: first, those describing the ocean surface directly in the spatial domain, then those describing the surface in spectral domain and finally hybrid methods combining the two. As we will show in the following section, spatial methods use a height map computed as a sum of periodical functions, and animated with a simple phase difference, in order to represent the ocean surface. Spectral approaches use a wave spectrum to describe the surface in the spectral domain and a Fourier Transform to obtain its transformation in the spatial domain. Finally the combination of the two, called hybrid methods, produces convincing surfaces that can be animated easily.

Spatial domain approaches

The main goal of spatial domain approaches is to represent the geometry of the water surface using a sum of periodical functions evolving temporally using a phase difference.

h(x, z,t) = -y 0 + Nw ∑ i=1 A i cos(k ix x + k iz z -w i t) (1)
where Nw is the total number of waves, A i is the amplitude of the i-th wave, k i = (k ix , k iz ) its wave vector, w i its pulsation and y 0 is the height of the free surface. The x-axis is oriented horizontally and points towards the coastline, the y-axis is vertical, and the z-axis is horizontal and aligned with the coastline. For each wave, the shape of the curve defined by the motion of a single point depends directly on the product between the amplitude A i and the wave number

k i = || k i ||. If k i A i < 0.
5, this path is similar to a trochoïd. If k i A i = 0.5, the shape is a cycloid. In all other cases (k i A i > 0.5), this path cannot represent a realistic motion (see Figure 2).

In order to obtain a realistic effect, the wave vector k i of each wave is computed using scattering relationship in deep water domain, i.e. supposing that the bottom of the sea is located at infinite depth:

k i = 2π/ gL i 2π (2)
submitted to COMPUTER GRAPHICS Forum (9/2011).

with g the gravitation constant and L i the wavelength of each individual wave.

The same idea was developed with a simple bump mapping approach, where normal vectors on a planar mesh are transformed using a sum of 20 cycloids [START_REF] Schachter | Long crested wave models[END_REF]. However, assuming that the bottom of the sea is at infinite depth limits the use of these methods since they don't include more complex phenomena such as breaking waves or waves refraction near the shore. Peachey [START_REF] Peachey | Modeling waves and surf[END_REF] introduces a depth parameter to compute the wave vector k i of each wave, using Airy wave theory:

k i = 2π/ gL i 2π tanh 2πd L i ( 3
)
where d is the depth of a point related to the bottom of the sea.

Fournier and Reeves [START_REF] Fournier | A simple model of ocean waves[END_REF] suggested modifying Gerstner's theory of waves, where water particles positions are given by:

x = x 0 -Ae ky0 sin(kx 0 -wt) y = y 0 -Ae ky0 cos(kz 0 -wt) (4)
with x (respectively y) the horizontal (resp. vertical) coordinate of a water particle at time t, x 0 and y 0 its coordinates at rest, A the wave amplitude, k the wave number and w the wave pulsation. Fournier and Reeves enhance this model by taking into account the transformation of the path of water particles following the topological changes of the sea bed, and by transforming their circular path into a more realistic elliptic motion. This method permits to control the waves' shape, more or less crested, through the use of different parameters, and therefore yields a more realistic result (see Figure 1).

Gonzato and Le Saec [START_REF] Saec | On modeling and rendering ocean scenes (diffraction, surface tracking and illumination)[END_REF] modify this model when the starting point of a plunging breaking wave is detected near the shoreline (i.e. if the wave's crest starts to curl over). This phenomenological modification results in the addition of two local functions applied to the wave's shape: a stretch function imitates Biesel law by progressively stretching the wave along its crest, and a plunging function simulates gravity.

Ts'o and Barsky [START_REF] Ts'o P | Modeling and rendering waves: wave-tracing using beta-splines and reflective and refractive texture mapping[END_REF] suggested that the refraction of waves could be represented by the principle of light refraction formulated by Descartes. Their approach, called wave tracing, consists in generating a spline surface by casting rays from the skyline in a uniform 2D grid, progressing with Bresenham's algorithm. The deviation of a ray is computed according to the depth difference of a cell to the next. However, a major drawback with this method is the lack of details on the generated surface when rays diverge significantly from a straight line, since in that case the number of rays defining the surface is too low. Gonzato and Le Saec [START_REF] Saec | On modeling and rendering ocean scenes[END_REF] address this problem by generating new rays in undersampled areas, offering a better representation of the ocean surface around bays or islands for instance. This method called "Dynamic Wave Tracing" can handle wave reflexion and diffraction due to obstacles. This approach was also used by Gamito and Musgrave [START_REF] Gamito | An acurrate model of wave refraction over shallow water[END_REF] to extract a phase map used in a parametric model, which can be animated easily. The height map representing the ocean surface can be rendered using enhanced ray tracing [START_REF] Saec | On modeling and rendering ocean scenes[END_REF] or sphere tracing [DCG07] methods.

GPU implementations

Series of periodic functions are particularly well suited to GPU computations, and in the last few years research works describing real time implementations have emerged.

Chen et al [START_REF] Chen | An efficient method for real-time ocean simulation[END_REF] use four sinusoids, computed in a vertex shader and transferred to a bump map in a pixel shader to simulate ripples. Salgado and Conci [START_REF] Salgado | On the simulation of ocean waves in real-time using the gpu[END_REF] describe a real-time implementation of Fournier's method [START_REF] Fournier | A simple model of ocean waves[END_REF] using a vertex shader. Schneider and Westermann [START_REF] Schneider | Towards real-time visual simulation of water surfaces[END_REF] compute a displacement map using Perlin noise in a vertex shader on the GPU to obtain interactive results. Isidoro et al [IVB02] use a precomputed mesh perturbed by four sinusoids with low frequencies in a vertex shader. Ripples are obtained by using a bump map combining multiple textures. When using a limited number of input functions, visually convincing surfaces are obtained in interactive time (see Figure 3). Cui et al [START_REF] Cui | Real-time ocean wave in multi-channel marine simulator[END_REF] follow the same approach combined with an adaptive tessellation of the surface using the method of Hinsinger et al [START_REF] Hinsinger | Interactive animation of ocean waves[END_REF] (described in Section 2.3).

Chou and Fu [START_REF] Chou C.-T | Ships on real-time rendering dynamic ocean applied in 6-dof platform motion simulator[END_REF] described a new GPU implementation for ocean simulation in order to take into account various interactions between the ocean surface and fixed or dynamic objects. The aim of this approach is to combine a particle system with a height-field obtained with a sum of sinusoids computed at each vertex of the surface mesh. Particles move according to the motion of each vertex but also to hydrodynamical forces [START_REF] Browing | A mathematical model to simulate small boat behaviour[END_REF][START_REF] Fang | An indigenous pc-based ship simulator incorporating the hydrodynamic numerical model and virtual reality technique[END_REF] due to solid objects interacting in the scene.

Adaptive schemes

In order to limit computation time, adaptive schemes have been proposed to limit computations only in visible areas and/or to reduce the number of periodic functions used to represent the surface dynamically, depending on the distance to the viewer. This approach consists in discarding high frequencies in distant areas, also limiting aliasing effects such as moiré patterns visible on the horizon. The "grid project" concept proposed by Johanson [Joh04] consists in projecting the pyramid of vision onto the height map representing the water surface. Distant areas are automatically sampled at low resolution, whereas high resolution is used near the viewer.

Finch [START_REF] Finch | Effective water simulation from physical models[END_REF] and Lee et al [START_REF] Go | An efficient algorithm for rendering large bodies of water[END_REF][START_REF] Go | A frustrum-based ocean rendering algorithm[END_REF] propose a Level of Details (LOD) tessellation by adapting the resolution of the surface to the distance between the viewer and the submitted to COMPUTER GRAPHICS Forum (9/2011). horizontal plane; using the angle between the camera and the surface, vertices outside the pyramid of vision are also discarded before rendering stage. The implementation by Lee et al provides a 40% gain in computation time compared to a fixed-resolution approach, and outperforms the implementation of Johanson [START_REF] Johanson | Real-Time water rendering -Introducing the projected grid concept[END_REF] (tests were conducted on a Pentium 4 at 3.0GHz and a GeForce 6600 GPU). Kryachko [Kry05] use vertex textures, by computing two height maps representing the global motion of waves and fine scale details. The resolution is based on the distance to the viewer, allowing for fine-tune computations (see Figure 3).

Fourier domain approaches

This type of representation consists in describing the ocean surface using a spectral distribution of waves, obtained from theoretical or measured data. The spatial representation is then computed using the most significant frequency components and an inverse fast Fourier transform (IFFT), giving a geometric characterization of the surface as a dynamic height map defined for each point X by:

h(X,t) = Ns ∑ i=1 h( k,t)e i kX ( 5
)
where Ns is the number of spectral components, k is the wave vector and h( k,t) is the amplitude of the Fourier component obtained from a theoretic wave spectrum.

General methods

This idea was proposed by Mastin et al [START_REF] Mastin | Fourier synthesis of ocean scenes[END_REF] with the Pierson-Moskowitz spectrum [START_REF] Moskowitz | A proposed spectral form for fully developped wind seas based on similarity theory of s.a kilaigorodskii[END_REF]. The amplitude of each Fourier component at time t = 0 is given by:

h0 ( k) = αg 2 16π 4 f 5 e -5 4 ( fm f ) 4 (6)
where α = 0.0081 is called Phillips' constant, g is the gravitation constant. The frequency peak fm is defined by:

fm = 0.13g U 10 (7)
with U 10 the wind speed measured at 10 meters above the surface.

Premoze and Ashikhmin [START_REF] Premoze | Rendering natural waters[END_REF] follow the same idea by using the JONSWAP spectrum [HBB * 73], a modified version of Pierson-Moskowitz's which reduces frequencies and thus raises waves' amplitudes. The amplitude of each Fourier component at time t = 0 in that case is slightly different:

h0 ( k) = αg 2 16π 4 f 5 e -5 4 ( fm f ) 4 e ln(γ)e -( f -fm) 2 2σ 2 f 2 m (8)
with:

σ = 0.07 if f fm 0.09 if f > fm
The method presented by Tessendorf [START_REF] Tessendorf | Simulating ocean waters[END_REF] was notably used in famous computer-generated scenes for Waterworld and Titanic productions. Again, this approach uses spectral components to describe the surface, computed by a Gaussian pseudo-random generator and a theoretic wave spectrum due to Phillips:

h0 ( k) = 1 √ 2 (γr + iγ i ) P h ( k) (9)
with γr and γ i defined as constants. The spectrum P h ( k) is given by:

P h ( k) = C e -1/(kL) 2 k 4 | k. w| 2 (10)
where C is a constant, k is the wave vector, k is the wave number, w is the wind direction, V is its speed and L = V 2 g . The choice of a random generator is justified by the Gaussian distribution of waves often observed in deep sea areas. In order to obtain fine details on the surface, each component is slightly perturbed by a noise function, producing more or less crested waves at any resolution (see Figure 4). Cieutat et al [START_REF] Gonzato J.-C | A general ocean waves model for ship design[END_REF] enhance this model in order to take in account water waves forces applied to a ship, implemented in a ship training simulator.

Although results obtained with this approach seem visually convincing for a distant viewer, when zooming towards the surface, waves' shapes tend to look unrealistic since the resolution of the heightmap is fixed. In that case it becomes necessary to generate a new surface using more spectral components. This problem is addressed by interactive methods proposed recently.

Level-Of-Detail and GPU implementations

submitted to COMPUTER GRAPHICS Forum (9/2011). Hu et al [HVT * 06] apply a LOD approach to Tessendorf's method by representing the ocean with two surfaces. The first one, with a high, fixed resolution, is animated using a displacement map stored in a vertex shader, while the second one is sampled adaptively and applied as a bump map stored in a pixel shader. This approach produces a large ocean surface in real-time by animating only visible parts (at approx. 100 frames/sec. on GeForce 3 GPU card). Mitchell [START_REF]Real-Time Synthesis and Rendering of Ocean Water[END_REF] implemented Tessendorf's method on GPU by only considering frequencies generating a significant perturbation of the surface. A white noise is first generated using Phillips' spectrum, then frequencies are divided in two sets. Low frequencies accounting for the global motion of waves are stored as a displacement map in a vertex shader. High frequencies, representing fine details, are stored in a normal map used for rendering. Since only a part of the spectrum is animated, a realistic ocean surface is obtained at interactive rates; another implementation by Chiu and Chang [START_REF] Chiu Y.-F | Gpu-based ocean rendering[END_REF] combine this approach with an adaptive tessellation method [START_REF] Johanson | Real-Time water rendering -Introducing the projected grid concept[END_REF] (see previous section).

An adaptive spectrum sampling is presented by Frechot [START_REF] Frechot | Realistic simulation of ocean surface using wave spectra[END_REF] in order to obtain a more realistic surface with capillary waves or riddles. The main idea of this approach is to resample the spectrum corresponding to high frequencies areas, depending on the distance to the viewer. Robine and Frechot [RF06] also described a real-time additive sound synthesis method applied to the ocean surface. Sound synthesis methods are commonly used to efficiently sum a large number of sinusoidal components called partials. Here, ocean waves are considered as partials by shifting from the frequency and time domains to the wave number and spatial ones.

Hybrid approaches

Hybrid approaches are a combination of spatial and spectral definitions, generating a geometric representation of the Figure 5: Ocean surface obtained in [START_REF] Thon | Ocean waves synthesis using a spectrum-based turbulence function[END_REF] surface while describing the components of wave trains in a realistic manner.

The method proposed by Thon et al [START_REF] Thon | Ocean waves synthesis using a spectrum-based turbulence function[END_REF]TG02] shows a combination of a linear superposition of trochoids, which characteristics are synthesized using Pierson and Moskowitz's spectrum. In order to get fine scale details, a 3D turbulence function is added to the surface; this method provides very realistic results, as shown on Figure 5.

Lee et al. [START_REF] Lee | Real-time simulation of surface gravity ocean waves based on the tma spectrum[END_REF] combine a superposition of sinusoids and the TMA spectrum (Texel, Marson and Arsole, based on Jonswap's) [START_REF] Bouws | Similarity of the wind wave spectrum in finite depth water: Part 1. spectral form[END_REF], creating a better statistical distribution of waves. It also offers better control for the end-user who can change parameters such as the bottom depth, thus enabling him to generate different types of water volumes (lakes, rivers, etc).

Xin et al [START_REF] Xin | Real-time and realistic simulation of large-scale deep ocean surface[END_REF] extend the method of [TG02] to simulate the effects of wind variations over the surface by modulating each spectrum frequency accordingly.

Hinsingert et al [START_REF] Hinsinger | Interactive animation of ocean waves[END_REF] apply a LOD scheme to the method of [TDG00] by reducing both the sampling resolution of the surface mesh and the number of trochoidal components depending on the distance to the viewer. This approach reduces the amount of computations for the ocean simulation and tends towards real-time rates (approximately 20 to 30 frames per sec. on a GeForce 2 GPU), by using only a subset of the components.

A real-time simulation method for ocean scenes was proposed by Lachman [START_REF] Lachman | An open programming architecture for modeling ocean waves[END_REF] with a framework representing the surface either in the spatial domain by combining a spectrum and a sum of sinusoids or by using the approach of [START_REF] Tessendorf | Simulating ocean waters[END_REF]. This method is highly controllable, allowing the user to modify parameters such as the bottom depth or the agitation of the sea (defined by the Beaufort Scale). A LOD representation of the surface is also implemented to reduce computation costs. The main idea consists in defining sev-eral resolution levels from the projection of the pyramid of vision on the surface, and meshing the surface accordingly.

Discussion

The main advantage of spatial domain approaches is their ability to produce a simple and fast simulation of the ocean surface, but they require a large number of periodical functions for visually plausible results. Several optimizations have been proposed such as GPU evaluation or adaptive schemes to reduce this number according to the distance to the viewer. However, using sine or cosine functions induces a too rounded shape of waves and the surface appears too smooth. Spectral domain methods address this problem by using oceanographic data directly and allow to disturb the surface according to physical parameters such as wind speed, which brings more realistic results. Unfortunately these methods lack from global control of ocean waves. In this context, hybrid approaches represent a good compromise between the visually plausible results obtained by spectral approaches and the global control offered by spatial domain methods, and allow to obtain fast and effective simulations of the ocean surface's dynamic behaviour. A complete summary of the methods presented in this section is shown on Table 1. However, all these methods only consider deep water phenomena, in which the ocean surface is being subjected to small perturbations. Indeed, in shallow water parametric or spectral approaches cannot faithfully reproduce ocean dynamics near coasts, e.g. breaking waves. To address this complexity, we have to focus on approaches that consider interactions and collisions between the ocean and the shore, which are presented in the next section.

Ocean dynamics simulation in shallow water

Navier-Stokes equations (NSE) are able to capture the dynamic complexity of a fluid flow. Incompressible flow is usually considered for large volumes of fluid like oceans:

∇ U = 0 (11) ∂ U ∂t + U∇ U + ∇p ρ -µ ∇ 2 U ρ -g = 0 (12)
with U = (u, v, w) the velocity of the fluid, µ its viscosity, p its pressure, ρ its density, and g representing gravity (0, 9.81, 0). Operator ∇ U (resp. ∇ 2 U) is the gradient (resp. Laplacian) of U and is defined by

∇ U = ( ∂u ∂t , ∂v ∂t , ∂w ∂t ) (resp. ∇ 2 U = ∂ 2 u ∂ 2 t + ∂ 2 v ∂ 2 t + ∂ 2 w ∂ 2 t
). The first equation guarantees mass conservation, i.e. the density of the fluid remains constant over time. The second one guarantees moment conservation: the acceleration ∂ U ∂t of the fluid is equal to the sum of the applied forces weighted by its density. Other formulations for fluid behavior include shallow water equations (or Saint-Venant equations), preferably used whenever the horizontal scale is greater than the vertical one.

There are two main ways of discretizing these equations. On the one hand, Eulerian approaches use a 2D or a 3D grid where the fluid goes from cell to cell. On the other hand, Lagrangian approaches are based on particles carrying the fluid, thus representing small fluid volumes. Hybrid techniques were also developed to combine these two techniques, adding small-scale details to Eulerian simulations such as bubbles or spray. An excellent tutorial on physicallybased simulation of fluids for Computer Graphics is presented by Bridson et al [BMFG06]. Adabala and Manohar [START_REF] Adabala | Techniques for realistic visualization of fluids: A survey[END_REF] proposed a survey of most physically-based fluid simulation techniques. Since numerous phenomena can be simulated by these methods (fire, smoke, lava, etc.) we will focus on liquids and more specifically on ocean waters.

Eulerian approaches

Kass and Miller [START_REF] Miller | Rapid, stable fluid dynamics for computer graphics[END_REF] were the first to use a physicallybased realistic approach to represent the ocean surface. This method consists in solving Saint-Venant equations in 2D in order to obtain a heightmap. This was later extended by Chen and Lobo [START_REF] Lobo | Toward interactive-rate simulation of fluids with moving obstacles using navier-stokes equations[END_REF] to solve NSE taking into account pressure effects, hence generating a more realistic surface modulation.

A full 3D resolution of NSE was introduced in the Computer Graphics community by Foster and Metaxas [FM96, FM97], inspired from a physical approach proposed by Harlow and Welch [START_REF] Harlow | Numerical calculation of timedependent viscous incompressible flow of fluid with free surface[END_REF] based on a uniform voxel decomposition of the 3D space. Velocity of the fluid is defined at the centers of each face of voxels; gradient and Laplacian are computed using finite differences between faces of adjacent voxels. Divergence at a given voxel is obtained from the updated velocities at its faces. In order to guarantee fluid incompressibility, the pressure field at a given voxel is modified according to the divergence. Virtual particles are placed in the voxel grid to extract the fluid surface, i.e. to discover its location, however the resulting surface does not look visually convincing. This problem was later addressed by Foster and Fedkiw [FF01] who represent it as an implicit, level-set surface evolving according to the fluid's velocity. Nevertheless, visual results show compressibility artifacts since a noticeable volume of fluid disappears during the animation.

In order to solve this problem, Enright et al [START_REF] Enright | Animation and rendering of complex water surfaces[END_REF] place particles above and below the surface, and advect them according to the velocity of the voxel they belong to. The surface is then computed by interpolating between the two implicit functions obtained from the locations of these particles. Since this approach called particles levelset method can be applied to all types of fluids, it became very popular and was widely used for many purposes, including the simulation of interactions between fluids and solids [START_REF] Carlson | Rigid fluid: animating the interplay between rigid bodies and fluid[END_REF]WMT05] or between different types of fluids [START_REF] Losasso | Multiple interacting liquids[END_REF]. The main drawback is high computational costs, which can be reduced by using an adaptive, octreesubmitted to COMPUTER GRAPHICS Forum (9/2011).

Model

Implementation Spatial Spectral Wave refraction GPU Level-Of-Details Schachter [START_REF] Schachter | Long crested wave models[END_REF] x Max [Max81]

x Fournier et al. [START_REF] Fournier | A simple model of ocean waves[END_REF] x Mastin et al. [START_REF] Mastin | Fourier synthesis of ocean scenes[END_REF] x Ts'o et al. [START_REF] Ts'o P | Modeling and rendering waves: wave-tracing using beta-splines and reflective and refractive texture mapping[END_REF] x x Gonzato et al. [START_REF] Saec | On modeling and rendering ocean scenes (diffraction, surface tracking and illumination)[END_REF] x Gonzato et al. [START_REF] Saec | On modeling and rendering ocean scenes[END_REF] x x Thon et al. [START_REF] Thon | Ocean waves synthesis using a spectrum-based turbulence function[END_REF] x x Premoze et al. [START_REF] Premoze | Rendering natural waters[END_REF] x Tessendorf [START_REF] Tessendorf | Simulating ocean waters[END_REF] x Schneider et al. [START_REF] Schneider | Towards real-time visual simulation of water surfaces[END_REF] x x Gamito et al. [START_REF] Gamito | An acurrate model of wave refraction over shallow water[END_REF] x x Hinsinger et al. [START_REF] Hinsinger | Interactive animation of ocean waves[END_REF] x x x Chou et al. [START_REF] Chou C.-T | Ships on real-time rendering dynamic ocean applied in 6-dof platform motion simulator[END_REF] x x x Lachman [START_REF] Lachman | An open programming architecture for modeling ocean waves[END_REF] x x x x Lee et al. [START_REF] Lee | Real-time simulation of surface gravity ocean waves based on the tma spectrum[END_REF] x x x Salgado et al. [START_REF] Salgado | On the simulation of ocean waves in real-time using the gpu[END_REF] x x

Table 1: Classification of the simulation methods for deep water presented in section 2

like structure [START_REF] Losasso | Simulating water and smoke with an octree data structure[END_REF] to refine the voxel grid only near the fluid-solid or fluid-fluid interface.

This approach permits to capture the dynamic behavior of fluid surfaces in a realistic way and can be used for oceanic scenes. Enright et al [START_REF] Enright | Animation and rendering of complex water surfaces[END_REF] simulate breaking waves by constraining the velocities in the grid using parametric equations [START_REF] Radovitzky R | lagrangian finite element analysis of newtonian fluid flows[END_REF]. Although realistic results are obtained, this approach can only handle limited types of waves (spilling or rolling waves). Mihalef et al [START_REF] Mihalef | Animation and control of breaking waves[END_REF] simulate breaking waves by constraining velocities inside the grid using the parametric approach of Thon et al [START_REF] Thon | Ocean waves synthesis using a spectrum-based turbulence function[END_REF] in 2D. The initial horizontal and vertical velocities of each element of fluid are given by:

u = Awe kz cos(kx) v = Awe kz sin(kx)
where, as in [START_REF] Thon | Ocean waves synthesis using a spectrum-based turbulence function[END_REF], A is the amplitude of a wave, k = (kx, kz) its characteristic vector and w its pulsation. The user can obtain any type of shore-break by choosing from a library of precomputed profiles. The full 3D simulation is then computed by extruding the desired profile along the parallel direction to the shore (see Figure 6). Thürey et al [START_REF] Thürey | Real-time breaking waves for shallow water simulations[END_REF] simulate breaking waves in realtime, by solving Saint-Venant equations in 2D. A breaking wave is obtained by detecting regions with high curvatures on the heightmap representing the fluid, and adding a new mesh to account for the water falling from the crest. Each vertex of this mesh is projected in the 2D grid and advected using the corresponding cell.

Lagrangian approaches

In Lagrangian approaches, the fluid is represented by a set of particles following physical laws. Particle systems were first introduced in the computer graphics community by Reeves [START_REF] Reeves | Particle systems : A technique for modeling a class of fuzzy objects[END_REF] to simulate natural phenomena such as water, fire, clouds or smoke. Miller and Pearce [START_REF] Miller | Globular dynamics: a connected particle system for animating viscous fluids[END_REF] simulate interactions between particles by connecting them with the aid of springs to represent attraction or repulsion forces between neighboring particles, hence simulating viscous liquid flows. Terzopoulos et al [START_REF] Terzopoulos | Heating and melting deformable models[END_REF] later extended this method to simulate morphing from a solid to a liquid by modifying the stiffness of each spring. Tonnesen [START_REF] Tonnesen | Modeling liquids and solids using thermal particles[END_REF] simulates the same kind of effects by solving heat transfer equations on the particles set.

Although realistic results are obtained with these methods, they are unable to simulate the inner dynamic complexity of fluids described by NSE. Stam and Fiume [SF95] introduced the Smoothed Particle Hydrodynamics (SPH) model in computer graphics, originally used in astrophysics to study the dynamics of celestial objects as well as their interactions [START_REF]A numerical approach to the testing of the fission hypothesis[END_REF], and formalized by Monaghan [START_REF] Monaghan | Smoothed particle hydrodynamics[END_REF] for fluids. In that case, NSE are simplified and linearized. By considering that each particle has its own mass and that their sum gives the overall mass of the fluid, Equation 11 can be omitted since the overall mass remains constant over time. In equation 12, the non-linear advection term, representing the fluid's transport related to its velocity in the Eulerian case, can be omitted: the fluid is transported by the particles themselves. Finally only one linear equation is necessary to describe the fluid's velocity U:

∂ U ∂t = 1 ρ (-∇p + µ∇ 2 U + ρg) (13)
Let f = -∇p + µ∇ 2 U + ρG represent the total amount of forces applied on a particle. The term ∇p accounts for pressure forces, µ∇ 2 U for viscosity forces, and ρG for exterior forces. The acceleration a of a particle is then given by:

a = ∂ U ∂t = 1 ρ ( f press + f visc + f ext ) (14)
where f press (resp. f visc and f ext ) represents pressure (resp. viscosity and exterior forces). The main idea in the SPH approach consists in defining particles as potential implicit surfaces (also known as blobs or metaballs) influencing their neighbors. A particle represents an estimation of the fluid in a given region rather than a single molecule. Force computations rely on the interpolation of any scalar value S i for a given particle i, depending on its neighbors:

S i = Np ∑ j=1 m j S j ρ j W (r, R) ( 15
)
where Np is the total number of particles, m j (resp. S j ) is the mass (resp. the scalar value) of particle j, r is the distance between particles i and j, R is the maximal interaction radius, and W is a symmetric interpolation function. The gradient ∇S i and Laplacian ∇ 2 S i are given by:

∇S i = N ∑ j=1 m j S j ρ j ∇W (r, R) (16) ∇ 2 S i = N ∑ j=1 m j S j ρ j ∇ 2 W (r, R) (17)
Equation 15 can then be used to compute the density of a particle i; pressure and viscosity computation will rely on equations 16 and 17.

The SPH model was extended by several authors [DC96, SAC * 99] to represent elastic deformations, lava flows, etc. by simulating heat transfer and varying viscosity. Müller et al [START_REF] Müller | Particlebased fluid simulation for interactive applications[END_REF] presented an extension to simulate low compressible liquids such as water. Clavet et al [START_REF] Clavet | Particle-based viscoelastic fluid simulation[END_REF] represent visco-elastic fluids by coupling particles with a mass-spring system; particles advection is governed by Navier-Stokes equations but also Newtonian spring dynamics, which slows the fluid down depending on springs stiffness. Another extension by Müller et al [START_REF] Müller | Particle-based fluid-fluid interaction[END_REF] represent interactions between fluids with different phases by modifying the viscosity between neighboring particles. This method can also simulate bubbles generated by heating, using varying densities for fluid particles to represent the amount of gasification.

However, two problems are inherent to the SPH approach. First of all, compressibility effects can be observed when the volume does not remain constant over time, yielding nonrealistic visualizations. Besides, a huge amount of particles is needed to simulate large volumes of water with fine-scale details, leading to high computation and memory consumption. These problems were addressed by several authors. Adaptive schemes were proposed to reduce the number of particles and limit computation and memory costs for simulating large volumes of fluid. Desbrun and Cani [START_REF] Desbrun | Space-Time Adaptive Simulation of Highly Deformable Substances[END_REF] merge or split particles according to their density. The overall mass of the system is kept constant by re-computing particle masses as soon as they are subjected to one of these operations. In order to guarantee symmetric interactions between particles with different masses, a shooting / gathering scheme ensures that attraction or repulsion forces are equal. Although this approach reduces computation costs, visual artifacts can be observed during animations because of instantaneous merging or splitting of particles near the surface. The adaptive scheme proposed by Hong et al [START_REF] House | Adaptive particles for incompressible fluid simulation[END_REF] consists in varying the size and number of particles according to their position relative to a fixed set of layers defined by the user in a preprocessing step. Finally, Adams et al [APKG07] obtain adaptively sized particles by defining merging or splitting processes, depending on the distance to the viewer or to the surface. This ensures that visual artifacts are avoided near the surface since only particles deep inside the fluid can be modified. This approach was implemented on GPU by Yan et al [YWH * 09] to simulate breaking waves in real-time.

Hybrid approaches

The main idea in hybrid approaches is to simulate the main body of fluid using an Eulerian method, and fine-scale details such as foam, spray or bubbles with a Lagrangian method. By adding small details, very realistic results are obtained, and interest for this approach is growing more and more with the development of efficient simulations. O'Brien and Hodgins [START_REF] O'brien | Dynamic simulation of splashing fluids[END_REF] couple an Eulerian method with a particle system to represent sprays. Navier-Stokes equations are solved in 2D, and sprays are generated depending on the magnitude of the vertical velocity at each cell; these particles are then advected using the velocity in the grid. The Eulerian simulation of Takahashi et al [TFK * 03] is coupled with particles generated in high curvature regions, then advected independently. Greenwood and House [START_REF] Greenwood | Better with bubbles: enhancing the visual realism of simulated fluid[END_REF] use a level-set approach [START_REF] Enright | Animation and rendering of complex water surfaces[END_REF] coupled with particles generated in high curvature regions, advected using the velocity of their corresponding cell. The friction of the fluid is also taken into account to generate bubbles.This method was later extended by Zheng et al [START_REF] Zheng | Simulation of bubbles[END_REF] by deforming each bubble based on surface tension, thus avoiding non-realistic spherical bubbles.

Kim et al [KCC * 06] extend an adaptive level-set approach [START_REF] Losasso | Simulating water and smoke with an octree data structure[END_REF] to generate particles according to the temporal variation of the volume of fluid in each cell. The main idea consists in using particles advected below the surface, transformed into water or air at the rendering stage. Since the number of transformed particles depends on the volume of water lost in a cell, this characterizes the turbulence in that cell and hence generates particles in highly perturbed regions.

Yuksel et. al [START_REF] Yuksel | Wave particles[END_REF] introduced the concept of wave particles to simulate waves and their interactions with solid objects. Wave particles are defined by a disturbance function characterized by an amplitude, a propagation angle and a maximal interaction distance. The fluid itself is represented by a height-field whose values are computed according to neighbouring wave particles. When waves collide with solid objects, propagation angles are re-computed according to the curvature at collision points and new particles are generated to obtain waves refraction.

Thürey et al [START_REF] Thürey | Animation of open water phenomena with coupled shallow water and free surface simulations[END_REF] proposed to couple 2D and 3D simulations using Saint-Venant equations solved with a Lattice-Boltzmann method [FDH * 87]. The 2D simulation accounts for global motion of the surface, but fine-scale details are represented in 3D. These two layers interact with each other to generate foam and sprays, by creating particles according to the velocity in each cell and surface tension at the air-water interface. This work was later extended with SPH to represent interactions between particles in [TSS * 07]. The same approach is followed by Losasso et al [START_REF] Losasso | Two-way coupled sph and particle level set fluid simulation[END_REF] to combine an Eulerian method with SPH particles whose number is computed from the divergence of the fluid's velocsubmitted to COMPUTER GRAPHICS Forum (9/2011). ity, thus simulating bubbles or sprays generated by breaking waves (see Figure 7).

Discussion

The main advantage of Eulerian approaches is their ability to simulate a large scope of different phenomena, explaining why they received much attention from the computer graphics community. Nevertheless, for fine-scale details such as spray or bubbles, NSE need to be finely discretized which in turn demands high computations and memory consumption. Another drawback is the use of fixed grids, forbidding the fluid to flow outside the grid.

On the other hand, Lagrangian approaches can be used to simulate a wide range of phenomena. Their main advantage is their ability to represent fine-scale details and to flow anywhere in a virtual environment, but a large number of particles is usually needed to obtain realistic results. This problem can be alleviated using adaptive split-and-merge schemes to reduce computation costs. However it is worth noticing that most of the computation time for one particle is spent in testing neighboring particles or other objects for collision. Therefore a broad-phase collision detection is usually implemented by storing particles in a virtual grid, meaning that Eulerian or Lagrangian approaches share common problems such as defining an appropriate size for the grid's cells. This is also illustrated by hybrid methods which produce realistic results by adding details to Eulerian approaches using particle systems. The literature presented in section 3 is summarized on Table 2.

Realistic ocean surface rendering and lighting

In the previous sections we presented different approaches to obtain a plausible shape of the ocean surface, in deep water or near the shoreline. This surface can then be rendered using water shaders implementing light reflection and refraction described by Fresnel equations. Nevertheless, the ocean's visual aspect is characterized by numerous interactions. Their impact is visible through several phenomena such as foam, sprays and light interactions, addressed by several methods in computer graphics. Some of them were already mentioned earlier, when the fluid simulation algorithm includes these phenomena directly (e.g. bubbles), However in most cases rendering is performed in a post-processing step. We focus on the following on different methods designed to enhance the realism of ocean scenes.

Foam and spray

Foam and spray rendering methods can be divided into two types: on the one hand, methods based on the computation of foam amount at one point on the ocean according to empirical models, and on the other hand, methods based on particle systems and rendered as point clouds.

Empirical models

Jensen and Golias [START_REF] Jensen | Deep-water animation and rendering[END_REF] compute the amount of foam at a given point according to its height: if the height difference with its neighbors is greater than a predefined threshold, foam is generated and rendered using a semi-transparent texture (see Figure 8). This method was extended by Jeschke et al [START_REF] Jeschke | A procedural model for interactive animation of breaking ocean waves[END_REF] to take into account the amplitude of ocean waves. The main drawback with this approach is encountered when trying to animate foam, since its motion does not follow the waves. Another problem arises from the empirical models that do not consider atmospheric conditions which are, in reality, the main cause of the apparition of foam. Oceanographic observations have shown for example that foam only appears when wind velocity exceeds 13km/h [START_REF] Munk | A critical wind speed for air-sea boundary processes[END_REF].

Premoze and Ashikhmin [START_REF] Premoze | Rendering natural waters[END_REF] compute the amount of foam based on wind velocity and the temperature difference between water and air. The user can control atmospheric conditions to induce more or less foam. However, results are limited by several constraints on the surface, and the animation is not visually convincing. Darles et al [START_REF] Darles | Accelerating and enhancing rendering of realistic ocean scenes[END_REF] extend this method with an animated texture, combined with other phenomena such as light attenuation due to spray particles in the air.

Particle systems

Peachey [START_REF] Peachey | Modeling waves and surf[END_REF] first proposed to use particle systems in order to represent spray generated by breaking waves. Wang et al [WZC * 06] extend this approach by describing breaking waves using a Lagrangian approach, and generating spray subsystems according to the velocity of water particles (see Figure 9). Holmberg and Wunsche [HW04] generate foam particles by considering the amplitude of the waves, and render them as cloud points. The same idea is used by other authors [START_REF] Jensen | Deep-water animation and rendering[END_REF][START_REF] Jeschke | A procedural model for interactive animation of breaking ocean waves[END_REF][START_REF] Chiu Y.-F | Gpu-based ocean rendering[END_REF] to generate spray particles according to the temporal variation of height at a given point.

submitted to COMPUTER GRAPHICS Forum (9/2011).

Model

Resolution Implementation Eulerian Lagrangian 2D-based Full 3D Incompressibility LOD Miller et al. [START_REF] Miller | Globular dynamics: a connected particle system for animating viscous fluids[END_REF] x x Terzopoulos et al. [START_REF] Terzopoulos | Heating and melting deformable models[END_REF] x x Kass et al. [START_REF] Miller | Rapid, stable fluid dynamics for computer graphics[END_REF] x x Tonnesen [START_REF] Tonnesen | Modeling liquids and solids using thermal particles[END_REF] x Although these methods provide realistic results, they also demand high computations since a large number of particles is needed; this proves difficult to handle when rendering large oceanic scenes.

Light-water interactions

Light-water interactions play an important role in the way we perceive ocean's color, however they must be approximated especially for real-time implementations. We use their order of approximation to classify existing methods, from strong simplifications of optics laws to highly accurate computations generating rippling caustics formed when light shines through ocean waves.

First order approximation

A first approach consists in rendering light-water interaction by applying geometrical optics laws, using Fresnel coefficients or Schlick's approximation [START_REF] Schlick | An inexpensive brdf model for physicallybased rendering[END_REF]. The Beer-Lambert law reduces the intensity I of a light ray by an exponential factor, depending on the covered distance d (i.e. the distance traveled by the ray from the light source to the intersection point) and an attenuation coefficient a:

I = I(0)e -ad (18)
where I(0) is the initial intensity of the ray. In the case of reflexion, intensity can be reduced according to the optical depth due to particles in the air. For refraction, the reduction comes from the attenuation coefficient of water, as implemented by Tessendorf [START_REF] Tessendorf | Simulating ocean waters[END_REF].

Gonzato and Le Saec [GS00] use Ivanoff's table defining the color of an ocean depending on its position on Earth [START_REF] Jerlov | Optical Aspects of Oceanography[END_REF]. This color takes into account reflected and refracted light, and in presence of submarine objects, a fast light absorption method is applied by using an ocean water absorption spectrum. In order to reduce computation costs and obtain realistic results in real-time, simpler methods and GPU implementations are often preferred. An environment mapping method can be enough to approximate reflexion and refraction effects. In both cases, the viewer is assumed to be far from the considered point, thus incident rays are considered parallels and reflected rays only depend on the surface's normal vector. This technique is commonly used in computer graphics, especially for ocean surface rendering

Multiple order approximation

When a light ray enters the ocean surface, a fraction is diffused, absorbed and reflected on organic particles in suspension near the surface. In order to represent the complexity of this phenomenon and compute the amount of light at any point inside the water volume, a Radiative Transfer equation (RTE) must be solved.

Arvo [START_REF] Arvo | Backward ray tracing[END_REF] propose to emit rays from light sources and to accumulate them in illumination maps to represent caustics. Iwasaki et al [IDN01, IDN03] use beam-tracing methods [START_REF] Heckbert | Beam tracing polygonal objects[END_REF]Wat90] to solve RTE by discretizing the water volume into illumination volumes formed by the intersection of refracted rays and the bottom of the sea, sliced into sub-volumes (see Figure 10). The amount of light bouncing back to the surface is computed by accumulating light in all traversed sub-volumes. By discretizing the water volume into horizontal, planar sheets, bouncing light can be computed by accumulating light at intersection points between rays and each sheet to obtain caustics. The photon mapping submitted to COMPUTER GRAPHICS Forum (9/2011). where aw(λ) is the attenuation coefficient of pure water for a given wavelength λ. Thus turbidity is directly related to the concentration of phytoplankton. This approach is able to represent realistic ocean colors according to their biological properties (see Figure 11).

Gutierrez et al [START_REF] Gutierrez | Visualizing underwater ocean optics[END_REF] simulate a wider range of phenomena such as inelastic diffusion of light rays, fluorescence effects due to phytoplankton particles and Raman diffusion, observed when an incident ray's wavelength is modified because of water properties. This model is able to characterize the visual impact of different kinds of sediments on the resulting image, and thus represent different ocean waters depending on their bio-chemical composition.

Finally another type of methods consider subsurface scat-tering inside water as participating media. Interested readers should refer to [START_REF] Perez-Cazorla F | Global illumination techniques for the simulation of participating media[END_REF] for an overview of these methods.

Discussion

Numerous methods are available in the literature to take different optical phenomena into account and increase the realism of oceanic scenes. In the case of foam and sprays, empirical methods can effectively simulate these phenomena according to the state of disturbance of the surface. Combined with particle systems, these approaches allow to obtain realistic details, however they require a large number of particles which induces an important memory cost and computation time at rendering stage. Moreover, empirical methods are usually efficient for deep water scenes only; to our knowledge there is no work dealing with realistic foam created by breaking waves. For light-water interactions, different methods were proposed to represent the complexity of these non-linear phenomena, yielding more and more realistic results. Moreover, recent approaches even consider physical and biology effects to simulate a wide variety of virtual environments. All these works are summarized on Table 3.

Conclusion

In this survey we have presented available methods in computer graphics for modeling and rendering oceanic scenes. The great amount of different works is inherent to the extreme diversity of the phenomena involved.

The first two sections of our survey focused on computer graphics models able to simulate the dynamical behavior of the ocean. We have seen that those methods are divided into two categories: on the one hand, methods usually dedicated to deep-water simulation, on the other hand fluid-based approaches trying to represent breaking waves near the shore. In the last section, we have seen different methods able to represent several phenomena involved in ocean rendering, namely foam, sprays and light-water interactions, that make for visual realism.

The next decade could see new methods emerging in an attempt to bridge the gap between deep-sea simulations and breaking waves representations; it would be necessary to put together different types of simulations on different scales. Scalable methods are also required for modeling and rendering stages in order to obtain real-time rates, which could include dynamic sampling of the simulation domain (as proposed by Yu et al [YNBH09] for rivers) and adaptive rendering models taking the visual impact of the considered phenomena into account.

Foam and Spray

Light

Figure 1 :Figure 2 :

 12 Figure1: Ocean surface obtained in[START_REF] Fournier | A simple model of ocean waves[END_REF]

Figure 3 :

 3 Figure 3: Real-time ocean simulation from [Kry05]

Figure 4 :

 4 Figure4: Ocean surface obtained in[START_REF] Tessendorf | Simulating ocean waters[END_REF]

Figure 6 :

 6 Figure6: Eulerian breaking waves simulation from[START_REF] Mihalef | Animation and control of breaking waves[END_REF]

Premoze

  et al [PTB * 03] introduced the Moving Particle Semi-implicit method (MPS) in computer graphics from submitted to COMPUTER GRAPHICS Forum (9/2011).

Figure 7 :

 7 Figure7: Hybrid simulation from[START_REF] Losasso | Two-way coupled sph and particle level set fluid simulation[END_REF]

Figure 8 :

 8 Figure8: Foam rendering from[START_REF] Jensen | Deep-water animation and rendering[END_REF]

Figure 9 :

 9 Figure 9: Spray rendering from [WZC * 06]

Figure 10 :

 10 Figure 10: Creation of illumination volumes from[START_REF] Iwasaki | An efficient method for rendering underwater optical effects using graphics hardware[END_REF]

  [SW01, JG01]. Baboud and Decoret [BD06] represent refraction by an environment map of the bottom of the sea. An alternative method was proposed by different authors [Bel03,HVT * 06] by mapping a sky texture onto the surface and considering this surface as perfectly specular. Recently Bruneton et al. [BNH10] proposed a GPU implementation of ocean lighting based on a hierarchical representation mixing geometry, normals and BRDF. The reflected light coming from the sun and the sky and the light refracted by the ocean are simulated by combining the BRDF model of Ross et al. [VRP05] and wave slope variance (i.e. normals) depending on the required level of detail.

Figure 11 :

 11 Figure11: Ocean surface rendering for a clear water from[START_REF] Premoze | Rendering natural waters[END_REF]

Table 2 :

 2 Classification of the simulation methods for shallow water presented in section 3

	x

submitted to COMPUTER GRAPHICS Forum (9/2011).

Table 3 :

 3 Classification of the realistic rendering methods presented in section 4viewers for their careful reading and comments about earlier drafts of this paper.

					-water interactions
			Empirical Particles First order Multiple order
	1986	Arvo [Arv86]			x
	1986	Peachey [Pea86]		x
	1993	Nishita et al. [NSTN93]			x
	2000	Gonzato et al. [GS00]			x
	2000	Premoze et al. [PA00]	x		x
	2001	Iwasaki et al. [IDN01]			x
	2001	Jensen [Jen01]			x
	2001	Jensen et al. [JG01]	x	x	x
	2001	Schneider et al. [SW01]			x
	2001	Tessendorf [Tes01]			x
	2003	Belyaev [Bel03]			x
	2003	Iwasaki et al. [IDN03]			x
	2003	Jeschke et al. [JBS03]	x	x
	2004	Cerezo et al. [CS04]			x
	2004	Holmberg et al. [HW04]		x
	2006	Chiu et al. [CC06]		x
	2006	Baboud et al. [BD06]			x
	2006	Hu et al. [HVT * 06]			x
	2006	Wang et al. [WZC * 06]		x
	2007	Darles et al. [DCG07]	x		x
	2008 Gutierrez et al. [GSAM08]			x
	2010	Bruneton et al. [BNH10]			x

submitted to COMPUTER GRAPHICS Forum (9/2011).

Acknowledgements

The authors thank C. Schlick and C. Rousselle for their careful proof reading. The authors also wish to thank the re-