Problem Set 4 CMSC 427 Distributed April 12, 2007 Due: Thursday, April 26 2006 Programming For this assignment you will write a simple ray tracer. It will be written in C++ without using OpenGL. For full credit, it must support the following features: • A camera with arbitrary position, direction, and orientation • Arbitrary image resolution • Triangle and sphere primitives • Ambient, directional, and point lights • Arbitrary materials defined by a color, Phong exponent, and specular fraction • Diffuse and specular shading, and mirror reflections • Cast shadows Note that the BMPImage library sometimes has problems with weird image resolutions, so you should stick with either powers of 2 (e.g. 64x64, 128x128, ...) or standard resolutions (e.g. 640x480, 1024x768, ...). The program must read from the command line the name of an input file describing the scene to be ray traced, the name of the output bmp file, and the image resolution. We have provided skeleton code that parses the command line and the scene input file. We have also provided sample input files, and the output files that the ray tracer should produce when using these as input.The input file format consists of a series of commands, each followed by a list of parameters. Blank lines and lines beginning with # are ignored. The supported commands are: Format Example Description camera eye x,y,z look at point x,y,z up vector x,y,z y field of view degrees camera 0.0 0.0 0.0 0.0 0.0 -100.0 0.0 1.0 0.0 30.0 Specifies the position, orientation, and direction of the camera. The image is defined to be 1 unit away from the camera in the direction the camera is facing. "eye" is the camera's position "look at point" is a point in the scene the camera is pointing at "up vector" gives the camera's orientation "y field of view degrees" is the angle from the top to the bottom of the image in the camera's up and down directions ambientLight intensity r, g, b ambientLight 0.1 0.1 0.1 Specifies an amount of light that is striking all objects in the scene. Each scene has at most one ambient light. directionLight intensity r, g, b direction x, y, z directionLight 0.3 0.0 0.0 1.0 1.0 1.0 Specifies a light coming into the scene from infinitely far away from the given direction ("direction" is the direction TO the light from any point in the scene). Direction lights can be shadowed. pointLight intensity r,g,b position x,y,z pointLight 0.0 300.0 0.0 30.0 10.0 -50.0 Specifies a point light source located at the given position. Since the light intensity attenuates with distance, you may want to make the initial intensity much larger than 1. Point lights can be shadowed. material color r,g,b Phong cosine exponent specular fraction material 1.0 1.0 1.0 50.0 0.0 Specifies the material properties for all triangles and spheres declared after this point in the file (until the next material command). "specular fraction" is the fraction of the final color that comes from the Phong specular highlight and the mirror reflection. The remaining fraction of the final color comes from the diffuse Lambertian shading. triangle vertex1 x,y,z vertex2 x,y,z vertex3 x,y,z triangle 5.0 0.0 -50.0 15.0 0.0 -50.0 15.0 10.0 -50.0 Specifies a triangle primitive with the given 3 vertices. sphere center x,y,z radius sphere 10.0 5.0 -47.5 1.0 Specifies a sphere primitive with the given center and radius.Points will be assigned as follows: • 40 Points- Render spheres and triangles with ray tracing under ambient light. For this you will need to shoot rays from the eye position through the pixels in the image and into the scene, and test for intersection against the primitives. The pixel color will be determined by finding the closest intersection, and multiplying that primitive's material color by the ambient light. • 30 Points- Add point and directional light sources with specular highlights and diffuse shading. Now, once you've found the closest ray intersection, you will need to compute a diffuse and a specular contribution to the final color from each light. The diffuse light contribution involves the angle between the surface normal and the light, while the specular light contribution involves the angle between the viewer and the light reflection, as well as the Phong exponent. The material's "specular fraction" tells what fraction of the final color should come from the specular light. The remaining fraction should come from the diffuse light, with the ambient light being added on top of these. Remember that point light intensity decreases proportional to the square of the distance from the light. • 20 Points- Add cast shadows. To implement this, when computing the diffuse and specular contributions from each light, you will need to first cast a ray in the direction of the light from the intersection point on the surface. If the ray intersects another object that is closer than the light, the point is shadowed from the light, and the light should not affect it. • 10 Points- Add mirror reflections. At each intersection point, recursively cast a ray from the point in the direction to the viewer reflected across the surface normal. This ray should not be cast if the recursion depth is greater than 5, or the surface material's "specular fraction" is 0. The light returned by this ray cast should be added to the specular light for this point. Extra credit: • Add anti-aliasing with super-sampling. Instead of casting one ray through each pixel in the image, cast several through different points in each pixel, and average the resulting colors. • Add refractions. Allow the index of refraction of materials to be specified in the scene file (your program should still be able to read scene files in the original format). You can assume the index of refraction of air is 1. When a ray intersects a surface, in addition to recursively casting a reflected ray, recursively cast a refracted ray in the direction given by Snell's law. The light returned by this ray should be added to the diffuse, specular, and ambient light.Notes: One thing you need to be careful of when writing this program is that, due to roundoff error, the intersection distance reported by your intersect routines will be slightly incorrect. This can cause a problem if you shoot another ray from the intersection point, since it might end up intersecting the same surface it's supposed to be coming from. To prevent this, you should