This chapter is really a survey. This just points out some algorithms but don’t explain them in detail.
- Types of Geometric Models
- Generic Operations
- Points, Planes, Lines and Rays
- Modeling and Viewing Transformations
3. Ray-Surface Intersections
3.1 Implicit Surfaces
3.2 Explicit Surfaces
3.3 Procedural Surfaces
Constructive Solid Geometry
Hierarchical Bounding Volumes
Stochastic Sampling and Distributed Ray Tracing
Rendering algorithms can be classified as analytic and discrete according to how they approach the aliasing problem. Discrete is better than analytic algorithms.
- super sampling
- adaptive sampling
- stochastic sampling (here we introduce)
2. Uniform point sampling
A review to uniform sampling as mentioned in paragraph 1.
3.Poisson disk sampling
Nonuniform distribution sample found in human eye called Poisson disk distribution, which replaces aliasing by noise.
4. Jittering a regular gird
This method produces good results and is well suited to image rendering algorithms, but it can remain small amount of aliasing as it is not as good as Poisson disk sampling.
5.Distributed ray tracing
Definition of distributed (probabilistic) ray tracing
If we regard the variables of the integration as additional dimensions, we can perform a Monte Carlo evaluation of the integrals by stochastically distributing the sample points(rays) in those additional dimensions.
How to calculate intensity I of reflected light at a point on the surface.
5.2 Depth of field
I don’t understand the formulas thoroughly.
Surface physics for ray tracing
1.Light and illumination
Introduces the physics mechanism why object show their color as you see.
Key words: photons, frequency, wavelength, spectra.
These physics principles is fundamental and each student with high school degree should know them.
2. Four mechanisms of light transport
- Perfect specular reflection
- perfect diffuse reflection
- perfect specular transmission
* total internal reflection
* optics for transmission
* Algebraic solution for T
* Geometric solution for T
- perfect diffuse transmission
3. Practical reflection and transmission
Section 2 only introduces the simplified model. There are another 2 problems to solve: rough surface and color shifting.
shading model can solve that.
4. A Shading Model
Here we get a shading model which describe the reflected light as a combination of diffuse and specular components. The result is that we get the light that correctly bounced off complex surfaces, and very realistic shading.
5. Faster Shading
The Hall shading model give us a more simple description of shading model which origins from the model above.
Essential ray tracing algorithms
2.Ray/sphere intersection and mapping
2.1 Intersection of the sphere – Algebraic Solution
calculate the intersection of the sphere and one ray from algebraic perspective
2.2 Intersection of the sphere – Geometric Solution
Use some geometric properties to deduce the computation amount.
2.3 Comparison of algebraic and geometric solution
Algebraic solution uses many replicate calculation like add first and subtract later while geometric solutions reduces this procedure. They in fact are internal unity.
I think there are others approaches in algebraic and geometric to speed up the ray tracing.
2.4 Precision problems
four methods are introduced in float-point calculations when solving intersections.
2.5 Spherical inverse mapping
map the sphere into one plane
3.1 Ray/plane intersection
Given a plane normal, origin and director of one ray, find the intersection on the plane.
Note: Two-sided plane and one-sided plane are different when finding the intersection.
3.2 Polygon Intersection
Finding if one point on a plane is inside a polygon in that plane.
- Jordan Curve Theorem: two types introduced in the book, it determines whether the intersection is inside the polygon.
3.3 Convex quadrilateral Inverse mapping
Obtain the location of a point within the convex quadrilateral. Just give the conclusion no derivation.
Triangle inverse mapping is a special case.
Tell you how to determine if the ray intersects the box but don’t tell you why.
5.Ray/Quadric intersection and mapping
5.1 Ray/Quadric Intersection
Give quadric equation to solve the intersection.
A guide to efficiency concern and floating point arithmetic imprecision.
5.2 Standard Inverse Mapping.
- others do not have std inverse mapping