1. 14th Lecture – Final Lecture
CPT 450 Computer Graphics
14th Lecture – Final Lecture

2. Rendering Goal – To produce realistic photo like renderings Used by
Designers
Engineers
Architects
Animators
People want to know what will it look like before they build it.

3. Visual cues to 3D geometry
Size (perspective – distant objects appear smaller)
Occlusion (one object covering another)
Binocular versus monocular vision
3D glasses
Shading
Very important

4. Physics of Light What happens when light hits an object? It can be:
Reflected
specular or diffuse
Transmitted and refracted (bent),
for dielectrics, i.e. water, glass…
Absorbed and then turned into heat. (Some radiation is then re-emitted, but mostly not in the visible wavelengths)

5. Types of Reflection
Math Models are used to approximate real-world phenomenon. Physics based.
Diffuse Reflection – a dull, matte surface emits light equally in all directions.
Most real surfaces are rough, on a microscopic level.
Lambert’s law
Kd * max(N * L, 0)
Specular Reflection - from smooth, shiny surfaces, i.e. a mirror.
Highlights are visible
Angle of incidence = angle of reflection R (for a mirror)
Ks * max(N * R, 0) ^ n
Models spread out this reflected light over a range of angles
Combinations are possible

6. Refraction Medium Index of Refraction Air n ~ 1 Water n = 1.33 Glass
Index of Refraction = Ratio of speed of light in a vacuum divided by the speed of light in the medium.
Snell’s Law: n1*sin(theta1) = n2*sin(theta2)
Occurs at the interface between 2 different materials
Medium
Index of Refraction
Air
n ~ 1
Water
n = 1.33
Glass
n = 1.4 to 1.5

7. Lighting sources Direct Indirect Point light sources
Directional lighting (sunlight)
Ambient Light
Indirect
Diffuse Reflection
Specular Reflection
Refracted light

8. Smooth Shading
Curved surfaces are approximated by many small flat polygons (facets)
Think of a mirrored disco ball
To smooth over the facets, interpolation is used.
Gourand shading (intensity interpolation)
Phong shading (normal vector interpolation)
Phong shading produces better rendering, but is slower than Gourand

9. 2 approaches Fast Rendering Ray Tracing
Represent curved surfaces as many small facets
Transform all facets on the 2D plane of projection, using a transformation matrix
Use algorithms to remove hidden surfaces
Ray Tracing
For each pixel on the screen, compute where a ray from the observer through that pixel, will intersect the scene and use that info to compute the brightness of the pixel
Slower rendering, but better quality

10. Ray Tracing Very complicated math, compute intensive
Recursive reflection and refraction (can be very time consuming)
Results: Beautifully rendered images
You can have multiple light sources, textured surfaces, and lots of options.

11. Ray Tracing algorithm For each pixel,
Compute the projector (ray from focus)
Intersect the ray with the scene
Compute illumination at visible point
Put resulting pixel into image

12. Try Ray Tracing software
You can download Stephen’s demo program.
You can Download Maya Personal Learning Edition from Alias for free for non-commercial use. See:
Maya is used by profession animators

13. VRML- Virtual Reality Modeling Language
Markup language for viewing 3D scenes
Browser plug-in required for viewing
Not as popular as before.

14. Final Exam 2 weeks from today
Like midterm. Open book and notes. Go through links on class schedule.