1. Ray Tracing Geometry
CSE 681

2. Camera Setup
CSE 681

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

4. Camera Setup =? Tan(q/2) = yres*pixelHeight/2N
pixelHeight = 2*Tan(qy/2) *N/yres =N
pixelWidth = 2*Tan(qx/2) *N/xres
CSE 681

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

6. Pixel Calculation Tan(q/2) = yres*pixelHeight/2N
pixelHeight = 2*Tan(qy/2) *N/yres
pixelWidth = 2*Tan(qx/2) *N/xres
Pixel AspectRatio = pixelWidth/pixelHeight
Coordinate (in u,v,n space) of upper left corner of screen = ?
CSE 681

7. 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)*PixelWidth*u + (yres/2)*PixelHeight *v
CSE 681

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

9. Interate through pixel Centers
scanlineStart = Eye +
w -
(xres/2)*PixelWidth*u +
(yres/2)*PixelHeight *v +
(pixelWidth/2)*u -
(pixelHeight/2)*v
pixelCenter += pixelWidth * u
scanlineStart -= pixelHeight * v
CSE 681

10. 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) {
closestObject = object
distancemin = distance }
CSE 681

11. Organization of Ray Tracer
If (distancemin > infinityThreshold)
pixelColor = background color
else
pixelColor = color of object at distancemin along ray d
ray
object
eye
CSE 681

12. Ray-Sphere Intersection - geometric
Knowns
C, r
Eye
Ray
Ray
t = |C-eye|
d+k = (C-eye) · Ray k s
t2= (d+k) 2 + s2 d r C
r2 = k2+ s2
eye t
CSE 681

13. Ray-Sphere Intersection - algebraic
x2 + y2 + z2 = r2
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 = r2
Expand squared terms and collect terms based on powers of d:
A* t 2 + B* t + C = 0
CSE 681

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