[Ray Tracing] 3 A Survey of Ray-Surface Intersection Algorithms

This chapter is really a survey. This just points out some algorithms but don’t explain them in detail.

2.Basic Geometry

  • 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


[RAY TRACING] 5 Stochastic Sampling and Distributed Ray Tracing

Stochastic Sampling and Distributed Ray Tracing

1. Introduction

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.

5.1 Shading

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.



[RAY TRACING] 4.Surface physics for ray tracing

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.


Real Life Experience

  • Cherish time, keep your bottom line. Sleep is important, do not negotiate with others on  this issue.
  • Don’t tell you have learnt something to others, talk is cheap and that is nonsense. Just do it and show the results to others, which is more persuasive.
  • Never tell others what you are going to do or what you are doing now if you are uncertain whether you can finish them. Tell them until you have completed it.
  • Don’t mix hard-working and laborious.
  • Life is harsh, life is harsh, life is harsh. Think about what you can do now, think about housing and other expenses when you enter into the society. Just concentrate on something worth.
  • How to get into work quickly without any interruption? Just don’t want to have a break before you start to work. You should have a break after a period of work or when it comes the ends of one day. Be productive!

[Ray Tracing] 2 Essential ray tracing algorithms

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.Ray/plane algorithms

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.

4.Ray/Box intersection

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.

  • circle
  • cylinder
  • cone
  • others do not have std inverse mapping