Course Overview

Class Description:

This recorded course provides a way for artists to learn and develop an intuition for utilizing mathematical tools in their work using industry-standard programs and methods. This course will not only showcase ways of utilizing math in Houdini but also focus on developing a mindset to solve new problems using math. Students will also learn some math-related tips and tricks to optimize their pre-rendered or real-time projects.

Learning Outcomes:

Students will leave this class with a fundamental understanding of different ways in which tools from Mathematics can be utilized for Motion Graphics, Shader Building, and Gameplay Programming. Students will learn to optimize some of their existing setups using Mathematics.

Course curriculum

    1. Resources

    1. 1. Divy Introduction

    2. 2. Course Introduction

    3. 3. Session 1 Overview

    1. 1. Introduction

    2. 2. Detail Wrangle

    3. 3. Multithreading Info

    4. 4. Point Wrangle

    5. 5. Number Wrangle

    6. 6. Profiling and the Benefit of Multithreading

    7. 7. Q&A: Wrangles, Thread Job Size

    1. 1. What are Functions?

    2. 2. Mathematical Functions

    3. 3. Examples of Functions

    4. 4. Sine Explained

    5. 5. Q&A: Sine and Radians

    6. 6. Connecting the Def of Sin with the Graph of Sin

    7. 7. Q&A: Names of Points and Lines

    8. 8. Cosine

    9. 9. Q&A: Relating Sin and Cos

    10. 10. Relating Sin and Cos using the Pythagorean Theorem

    11. 11. Tangent

    12. 12. Q&A: Tangent, Infinity and Quadrants

    13. 13. Function Visualizer HDA

    14. 14. Manipulating the Input

    15. 15. Manipulating the Output

    16. 16. Composing Functions

    1. 1. Starting to make masks

    2. 2. Remapping Sin (2 ways)

    3. 3. How to use our functions [Lerp]

    4. 4. Interpolation Explained

    5. 5. Q&A: Lerping Data Types

    6. 6. Controlling the Interpolation Bias

    7. 7. Translating between the Func Visualizer and Vex

    8. 8. Using it in a setup

    9. 9. Radial Functions

    10. 10. Arc Functions

    11. 11. Q&A: Why PI/ 6?

    12. 12. Q&A: Range of Arc Functions

    13. 13. Arc Tan

    1. 1. Intro to Polar Coordinates

    2. 2. Q&A: Cartesian vs Polar

    3. 3. Brain Exercise

    4. 4. Drawing with Polar Coordinates

    5. 5. Brain Excersice 2

    6. 6. Distance Explained with Polar Coords

    7. 7. Atan explained with Polar Coords

    8. 8. Q&A: Slope and Atan, Atan2

About this course

  • $80.00
  • 175 lessons
  • 9.5 hours of video content

Course Teaser

Session 1

Understanding Functions & Number System

In this session, we will develop a solid foundation for the number system and mathematical functions. With the help of real work examples, we will wrap our heads around topics like complex numbers, cartesian & polar coordinates, mapping of mathematical functions in different dimensions, and interpolation with their use cases in Motion Graphics and Shader Building.
  1. Introduction
  2. Number System
  3. Brief Introduction to Complex Numbers
  4. Introduction to Mathematical Functions
  5. Algebra of Functions
  6. Function composition
  7. Use cases of some common functions
  8. Cartesian Coordinates
  9. Developing mindset for the transformation of space using Polar Coordinates
  10. Linear Interpolation & Smooth Step
  11. Group Practice Session

Session 2

Understanding Vectors

In this session, we will learn about vectors. Vectors are one of the most important concepts in computer graphics. They are the building blocks for most of the 2D and 3D motion graphics art pieces. We will discuss different ways in which we can utilize vectors for problem-solving and art direction. We will also briefly look into topics from multivariable calculus to gain insights into vector fields.
  1. Introduction to Vectors
  2. Point Vs Direction
  3. Magnitude & Direction of Vectors
  4. Resolution of Vector
  5. Algebra of Vectors
  6. Dot Product
  7. Cross Product
  8. Vector Fields
  9. Divergence & Curl
  10. Gradient Vectors
  11. Group Practice Session

Session 3

Understanding Quaternions

In this session, we will work with Quaternions and discuss their significance over Euler rotations. Through this session, we will build a relationship between quaternions and complex numbers that can be helpful for debugging our quaternion-based algorithms. We will learn how they can be used to rotate objects in 3D space and help us overcome some of the limitations of matrices.
  1. Introduction to Quaternions
  2. Euler Angles Vs Quaternions
  3. Relationship between Quaternions and Complex Numbers
  4. 3D Rotation using Quaternions
  5. Euler Angles to Quaternions
  6. Quaternions to Euler Angles
  7. Quaternion to Rotation Matrix
  8. Quaternion Interpolation
  9. Other useful Quaternion Functions 
  10. Group Practice Session

Session 4

Understanding Transformation of Matrices

In this session, we will utilize what we have learned till now to understand the concept of Matrices. We will discuss the need for matrices and their use cases. We will also take a deep dive into the process of packing transformations into a matrix and then unpacking for all sorts of use cases. Overall, we will try to get comfortable with using matrices by understanding them mathematically and conceptually.
  1. Introduction to Matrices
  2. Matrix Multiplication
  3. Unpacking the Matrix
  4. Basis Vectors
  5. Cylindrical & Spherical Coordinate Systems
  6. Transformation using Matrices
  7. Quaternions and Matrices
  8. Matrix Interpolation
  9. Use cases of Matrices in Computer Graphics
  10. Recap


Divyansh Mishra

Technical Artist

Divy is a Technical Artist mainly focused on tool building and automation. He is currently a Technical Artist Engineer at Amazon Robotics. His main tools of choice are Houdini, Unreal Engine & Substance Designer.



  1. Computer (Please see SideFx system requirements)
    2. A second monitor is recommended, but not necessary
  2. Redshift will be used for the rendering
  3. Houdini (Apprentice License is free)
  4. It is recommended that students take HS-001: Free Quickstart & HS-115: VEX Weekend Bootcamp before taking this course.


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Multi-Session Courses
Students may request a refund up to 1 day before the start of the course. Students may also withdraw from Multi-Session Courses at any time and are entitled to a pro-rated refund. The withdrawal date must be 1 day before the next class they intend to drop.

On-Demand Courses
All on-demand courses are non-refundable.

How to Drop a Class
Please send a request to drop a class via email to [email protected].
Your written request to drop any or all of your classes must include:
  1. Student’s full name
  2. Name of the course(s) being dropped


“When you learn math, you appreciate it more and more after you get past the immense hatred and headaches of learning math. 😂 @HoudiniSchool helped me considerably on that journey recently. Divy’s “Math for Artists” class has been a god send. He teaches it incredibly well.”

David Torno

“@Divy Amazing class! Thank you for sharing your knowledge with us!”

Armin Lotfi

“Was a great class @Divy ! The explanations were very clear and easy to understand overall. You should edit a version of this video and give it away to high schools Nice job!”

Paul Colton

See you in Class!