1. Simple Texture Mapping
and
Simple Ray-Tracing

2. Texture Map Each pixel in a texture map is called a Texel
Each Texel is associated with a (s,t) 2D texture coordinate
The range of s, t is [0.0,1.0] due to normalization

3. Simple Mapping
Texture Coordinates
Projection Coordinates

4. Simple Mapping
Texture Coordinates
Projection Coordinates

5. Simple Mapping

6. Basic File Structure Add texture coordinates v1 x1 y1 z1 u1 v1

7. Texture Filtering
Get an interpolated value from near four neighbors

8. Bilinear Interpolation

9. Perspective Correction
Linear Interpolation
of Texture Coordinate
Corrected Interpolation

10. Perspective Correction
Let’s assume that the viewport is located 1 unit away from the projection center

11. Perspective Correction
Compare linear interpolation in screen space

12. Perspective Correction

13. Perspective Correction
We can interpolate arbitrary parameters of a surface on the screen coordinates in the linear fashion
Use s instead t !
(ex) Gouraud shading, Phong normal . . etc

14. Perspective Correction
Further reading
(Perspective correction with Z-buffering)

15. Ray Tracing Concept
eye
view plane
Binary Tree

16. Ray Tracing Procedure
For each ray r from eye to pixel, color the pixel the value returned by the function: ray_cast(r)
ray_cast(r) {
s  nearest_intersected_surface(r);
p  point_of_intersection(r, s);
u reflect(r, s, p);
v refract(r, s, p);
c  phong(p, s, r) +
s.kreflect  ray_cast(u) +
s.krefract  ray_cast(v);
return(c); }

17. Ray Tracing Procedure s  nearest_intersected_surface(r);
Use geometric searching to find the nearest surface s intersected by the ray r
p  point_of_intersection(r, s);
Compute p, the point of intersection of ray r with surface s
u reflect(r, s, p); v refract(r, s, p);
Compute the reflected ray u and the refracted ray v using Snell’s Laws

18. Ray Tracing Procedure phong(p, s, r) s.kreflect  ray_cast(u)
Evaluate the Phong reflection model for the ray r at point p on surface s, taking shadowing into account
s.kreflect  ray_cast(u)
Multiply the contribution from the reflected ray u by the specular-reflection coefficient kreflect for surface s
s.krefract  ray_cast(v)
Multiply the contribution from the refracted ray v by the specular-refraction coefficient krefract for surface s

19. Reflection and Refraction
Reflected and refracted rays are computed using Snell’s Law
surface
normal
reflected
ray
incident
ray
surface
refracted
ray

20. Shadowing
If any object intersects the shadow ray between the surface and the point light source, the surface is in shadow w.r.t. that light source
blocked ! u L N r

21. Surface Intersection
Ray equation
ray path

22. Surface Intersection For sphere,
If the discriminant is negative, the ray does not intersect the sphere. Otherwise, intersection coordinates are obtained using smaller s.