Abstract

Impacted by the current pandemic, we have unprecedentedly sheltered in place for months. Life under Covid-19 has separated us from the gorgeous nature. Ocean waves, as one of the signature views for us to remember California, is the subject of our animation project. In this project, we will simulate ocean wave motions on a mesh surface, and apply texture mapping and shading on it in real-time.

• Our first problem is to simulate ocean wave motions on a mesh surface. To implement this, we dynamically updated each point’s position by summing up frequency(cosine) curves. Then, we changed the coefficients of the curves to customize each wave’s wavelength, amplitude, speed and direction. Finally, we interpolated over all waves to render a complete wave surface.
• Our next problem is to render a well-textured wave surface in real time. We made real-time animation by keeping track of the time variable. To incorporate shader programs in our project, we used Gerstner formula to compute vertex normals and tangents on the wave surface. Next, we implemented multiple shaders including bumping, texture mapping, and phong shading that well accounted for water reflection and refraction.

Technical Approach

Part I: Wave Surface Mesh

1. Basic Code Structure

Moving forward from project 4, we added two new objects to represent waves and wave surfaces. The resulting classes are as following:

• Wave: each has attributes of wavelength, amplitude, speed and direction
• WaveSurface: stores a list of waves on the surface; has methods to updated vertex position and compute vertex normal and tangent vectors.
• Adapted Cloth Object: renders and stores a WaveSurface instance; keeps track of the dynamic time

2.Position Update Algorithm

The basic idea of Gerstner Waves is that each vertex position on the surface is the sum of all frequency(cosine) curves at this point at a specific time. We have decided to apply Gerstner's way of computing vertex normals and tangents instead of simply using mesh geometry. After careful testing, we believe that this new approach will give us a more natural shading effect later when we complete shader programs.

3. Results

Part II: Real-time Rendering

1. Time-Tracking Algorithm:

After we've implemented point position update, we add a time attributde to Cloth so that we can keep track of elapsed time and make the surface move dynamically. More specifically, we will update the time variable by adding delta_t to it each time we call Cloth::Simulate. To map a plastic layer onto the surface, we choose the ambience color to be dark blue and use the original phong shader for now. Since the wave surface is displaced horizontally, we adjusted the light posiiton to be (-0.5, -0.5, -2). Below are pictures of how the plastic surface varies according to different values of wave parameters.

2. GUI

In GUI, the user is able to set the following values: number of waves on the surface, steepness of the waves, all parameters of the first dominating wave. Waves exceeding the number of 1 will be generated using default parameter values. In the Cloth header file, we set the number of waves to be 5 at maximum. The default parameter values vary across different waves. We are not rendering more than 5 waves because we have observed that too many waves will destruct the flow of the wave surface.

Part III: Shaders

1. Reflection. We first try to reflect the skyview onto the wave surface by constructing a "sky box" using cubemap. To account for the fact that the sky is endlessly wide, for all 6 faces of the cubmap, we use the same seamless skyview image. With only reflection, the sea surface looks like a mirror. To make it look more natural, we decide to decrease the value of alpha to be 0.5 after rigorous testing.

2. Refraction. To account for the refraction between water and air, we adopt ior(index of reflection) to be 1.33 and compute eta to be 1.0/1.33. The reflected ray is then calculated and used for tecture sampling.

3. Combining water refraction and surfrace reflection of sky

In the previous part, we observe that if we only use refraction, the water body would appear to have very little depth. In order to interpolate between refraction and reflection, we test out the resulting surface with different scalars and decide to scale refraction by 0.15 before adding them together. Again we set the alpha to be 0.5 to take care of the water transparancy.