Ray Tracing Geometry CSE 681 Camera Setup CSE

Ray Tracing Geometry CSE 681

Camera Setup CSE 681

Camera Setup “up” vector n v w View direction u Can be formed as cross product of view vector and up vector CSE 681

Camera Setup =? Tan(q/2) = yres*pixel. Height/2 N =N pixel. Height = 2*Tan(qy/2) *N/yres pixel. Width = 2*Tan(qx/2) *N/xres CSE 681

Screen Placement How do images differ if the resolution doesn’t change? CSE 681

Pixel Calculation Tan(q/2) = yres*pixel. Height/2 N pixel. Height = 2*Tan(qy/2) *N/yres pixel. Width = 2*Tan(qx/2) *N/xres Pixel Aspect. Ratio = pixel. Width/pixel. Height Coordinate (in u, v, n space) of upper left corner of screen = ? CSE 681

Pixel Calculation Coordinate (in u, v, n space) of upper left corner of screen = ? Assume virtual screen is one unit away (N=1) in w direction Eye + w - (xres/2)*Pixel. Width*u + (yres/2)*Pixel. Height *v CSE 681

Pixel Calculation Coordinate (in u, v, n space) of upper left pixel center = ? Eye + w - (xres/2)*Pixel. Width*u + (yres/2)*Pixel. Height *v + (pixel. Width/2)*u - (pixel. Height/2)*v CSE 681

Interate through pixel Centers pixel. Center = scanline. Start = Eye + w(xres/2)*Pixel. Width*u + (yres/2)*Pixel. Height *v + (pixel. Width/2)*u (pixel. Height/2)*v pixel. Center += pixel. Width * u scanline. Start -= pixel. Height * v CSE 681

Organization of Ray Tracer For each pixel { Form ray from eye through pixel distancemin = infinity For each object { If (distance=intersect(ray, object)) { If (distance< distancemin) { closest. Object = object distancemin = distance } } CSE 681

Organization of Ray Tracer If (distancemin > infinity. Threshold) pixel. Color = background color else pixel. Color = color of object at distancemin along ray d eye ray object CSE 681

Ray-Sphere Intersection - geometric Knowns C, r Eye Ray t = |C-eye| d eye d+k = (C-eye) · Ray k r s t 2= (d+k) 2 + s 2 C t CSE 681 r 2 = k 2+ s 2

Ray-Sphere Intersection - algebraic x 2 + y 2 + z 2 = r 2 p = eye + t*Ray Substitute definition of p into first equation: (eye. x+ t *ray. x) 2 + (eye. y+ t *ray. y)2 + (eye. z+ t *ray. z) 2 = r 2 Expand squared terms and collect terms based on powers of d: A* t 2 + B* t + C = 0 CSE 681

Determine Color Use z-component of normalized normal vector FOR LAB #1 Clamp to [0. 3. . 1. 0] N object. Color*Nz What’s the normal at a point on the sphere? ray eye CSE 681