by Jett Andersen

This is my final project for Columbia's computer graphics course (Spring 2014). It features soft shadows and lambertian shading, and is my first attempt at programming with modern OpenGL.

Contents I. Directions II. Features III. Implementation IV. Results V. Sources

I. Directions To compile, run make. To run, type bin/main. Must be compiled on a Mac with OS X 10.7 or higher and an Nvidia card supporting OpenGL 3.2.

wasd - Move camera (with strafing) Arrow keys - Move camera (with rotating) xz - Rotation meshes

II. Features I implemented an interface for exploring a 3D world with three degrees of freedom. The world features soft shadows from multiple point light sources, and surfaces with blinn phong shading.

III. Implementation I implemented this program entirely with modern OpenGL 3 features, abandoning the fixed function pipeline with which we began the class.

My algorithm for shadow mapping is slightly unique, leading to some strange behavior. I implemented it with simple orward rendering: for each light source, I render the shadowmap from its perspective, render the scene as if that light were the only light, and then add my results for each light. The unique part is in rendering the shadowmap. The space that is visible to a point light is typically recorded in a cubemap, treating the world around it as lying on a cube. I decided to record the point light's view in a single texture that treated the surrounding world as if it were on a sphere. To do this, I converted each x, y, z point relative to the light to polar coordinates, and stored the rho value at the texture UV coordinates (theta, phi).

I achieved soft shadows using a simple percentage-closer filter that sampled depth values locally, averaged the boolean mask that represented whether or not a pixel was visible to the light, and scaled the shading by that average.

IV. Results My results are clearly soft shadows, albeit with some aliassing problems due to the shadowmap's resolution. My radial method produces interesting artifiacts that, although detracting from the quality of the result, did give me a much better understanding of rasterization. The first of these is that a few rare angles cause a strange pattern of triangles to be shaded, and is due to wraparound errors when the triangle crosses a "seam" on my projection, and the texture samples incorrect, usually empty, values within the triangle. The second is that some viewing angles show light slipping through the mesh, and I believe this is due to linear rasterization not mixing nicely with a nonlinear texture projection. As a result, the center of large triangles can seem to curve through small triangles from the perspective of the fragment shader.

V. Sources For learning modern OpenGL, I used the tutorials located at opengl-tutorial.org. They do have a section on shadowmapping, but this was not useful for me, given that I was interested in point light shadow mapping and soft shadows.

I learned about percentage closer filtering from the paper located in the Sources directory titled ReevesPCF.pdf.