Math for 3D/Games Programmers FREE
Wojt Sterna
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日期和时间 |
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09/23(2024) |
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11/22(2024) |
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The “Math for 3D/Games Programmers” course is the result of my many months of work on a video course which, on the one hand, is intended to be very practical, and on the other hand explains how the theoretical background of the topics discussed, including from time to time delving a little deeper into derivation of some mathematical formulas important for game/3D programmers.
On the one hand, there are a lot of very solid and often voluminous books on 3D mathematics for programmers available on the market (requiring a lot of time to work through them), although they contain few practical examples – reading dry formulas without observing them in action can make them very difficult to understand. On the other hand, we have plenty of free mathematical programming libraries for solving specific programming problems, but whose inner workings can be “dark magic” to us. This course is in the middle – we learn as much theory as needed to understand a given topic, and at the same time we learn this theory on specific sample programs.
Find out more here:
https://wojtsterna.com/math-for-3d-programmers
https://wojtsterna.com
Table of Contents:
(in this package only FREE chapters are included)
1. Trigonometry (FREE)
Trigonometric Functions
Generic Sine Function
Polar Coordinates
Generating Points on Circle
Spherical Coordinates
Generating Points on Sphere
2. Complex Numbers (FREE)
Definition
Operations
Trigonometric Form
Exponential Form
3. Vectors (FREE)
What is a Vector
Vector Creation from Two Points
Vector as a Point
Addition
Subtraction
Linear Interpolation
Vector Length
Normalization
Normal Vector
Perpendicular Vectors in 2D
Dot Product
Vector Projection
Cross Product (Perpendicular Vector in 3D)
Point in Triangle (in 2D)
Normalized Vector Compression
4. Geometrical Objects Equations (FREE)
Line
- Line Equation
- Implicit Equation
- Parametric Equation
Circle
- Implicit Equation
- Parametric Equation
Sphere
Plane
- Implicit Equation
- Parametric Equation
Triangle
- Barycentric Coordinates
Equations Optimization
5. Matrices and Transforms I (PAID)
Matrices
Transforms
Transforms and Matrices
Image Rotation on GPU
Point Projection onto a Plane
6. Matrices and Transforms II (PAID)
Rotation Matrix About Any Axis
Column and Row Order
Scale-Rotate-Translate (SRT) and Hierarchy
Camera and Projection Matrices
Basis and Basis Change
Normal Vector Transformation
Plane Transformation
7. Quaternions (PAID)
What is a Quaternion
Rotation About Any Axis
Quaternion, Matrix and Euler Angles
Spherical Linear Interpolation (Slerp)
Gimbal lock
8. Derivatives (PAID)
What is a Derivative
Numerical Calculation
Analytical Calculation
Function Extrema
Derivative of Parametric Function
Partial Derivatives and Gradient
Least Squares Method
Gradient Descent Algorithm
Tangent Space
9. Integrals (PAID)
What is an Integral
Numerical Calculation
Analytical Calculation
Motion Equation Integration
Double Integral
Analytical Integration Example
Numerical Integration Example
