Computer Graphics: Programming, Problem Solving, and Visual Communication Steve Cunningham California State University Stanislaus and Grinnell College PowerPoint Instructor’s Resource

Nonpolygon Graphics Techniques that lie generally outside the OpenGL graphics model

A Number of Techniques… Ray tracing Ray casting Iterated function systems –Contraction mappings –Generating functions –Mandelbrot and Julia sets

Ray Casting Create a “virtual screen” and generate a ray from the eye point through each point on the screen Compute what each ray hits in the screen, and color the pixel the appropriate color

Ray Casting (2) The value of ray casting lies in being able to compute whatever the ray hits This may be a computation of a single hit or may involve many things along the ray, as in volume rendering

Ray Tracing Ray tracing starts with ray casting, but includes the possibility of generating new rays when the original ray hits something –Reflection rays –Refraction rays –Rays to light sources

Ray Tracing (2) Ray tree, with reflection R, refraction T, and light L rays shown Example ray-traced image, from POVRay

IFS - Contraction Mapping Generate a number of random points (in either 2D or 3D space) Apply a recursive stochastic function that maps the point into other points After a given number of steps, stop the recursion and plot the points

Contraction Mappings (2) Example: Sierpinski Gasket Example: fern

IFS - Generating Functions Blancmange functionDragon curve

IFS - Mandelbrot and Julia Sets Mandelbrot setJulia set