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Course: Pixar in a Box > Unit 6
Lesson 2: Mathematics of Rendering- Start here!
- 1. Ray tracing intuition
- 2D rendering intuition
- 2. Parametric form of a ray
- Parametric ray intuition
- 3. Calculate intersection point
- Solve for t
- 4. Using the line equation
- Ray intersection with line
- 5. 3D ray tracing part 1
- Ray intersection with plane
- 6. 3D ray tracing part 2
- Triangle intersection in 3D
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Start here!
Overview of this lesson
Ready to dive into some math?
In this lesson we are going to explore the most fundamental calculation a ray tracer performs: ray object intersection.
Since objects in our scenes are modeled using millions of tiny triangles, each intersection is betweena ray and a triangle.
In this lesson we'll start with the a simpler version of this problem, the intersection of a ray and a line in 2D:
Finally we'll extend these ideas from two dimensions to work in three dimensions. By the end of this lesson we'll need to solve a pretty meaty system of equations with 4 unknowns:
Sound like fun? By the end of this lesson you can say you have a basic understanding of ray tracing along with a mathematical view of the underlying geometry which makes it all work. How cool is that?
What do I need to know before starting?
- You should be familiar with the slope-intercept form of a line. Click here to review a video or click here to do an exercise.
- We'll also be using the parametric form which requires you understand weighted averages of two points. We covered weighted averages of two points in the Environment Modeling lesson.
- Finally we'll need weighted averages of three points which we covered in the Character Modeling lesson.
- You should also have experience solving systems of equations.
Okay, you're ready to go!