Maths for Artists

HS-223: Maths for Artists

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 s

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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
1. 1. Introduction
2. 2 Understanding Scaling
3. 3. Scaling with the Unit Circle
4. 4. Basics of Vectors
5. 5. Vectors in 1D
6. 6. Vectors in 2D
7. 7. Representing Vectors as Arrows
8. 8. Position and Direction Vectors
9. 9. Representing a Rectangle with Vectors
10. 10. The Importance of Vectors
1. 1. Adding Vectors
2. 2. Building a Setup
3. 3. Moving Between Positions
4. 4. Moving Objects
5. 5. Normalized Vectors
6. 6. Animating Movement
7. 7. Q&A: Why Normalize?
8. 8. Adding Direction Vectors
9. 9. Adding Wind to the Animation
10. 10. Q&A: Moving Flippy
11. 11. Quick Topic Recap
12. 12. (not) Multiplying Vectors
13. 13. Vector Resolution
14. 14. Q&A: Splitting Vectors
15. 15. Another Explanation
1. 1. Explaining Dot Product
2. 2. How Dot Product is Used
3. 3. Q&A: Splitting Vectors
4. 4. Setup 1 - Light Mask
5. 5. Setup 2 - Objects Looking at Other Objects
1. 1. Explaining Cross Product
2. 2.. Q&A: Placement of Cross Vector
3. 3. An Intuition for Cross Product
4. 4. Flipping the Direction of Cross Product
5. 5. Using the Right Hand Rule to Determine Direction
6. 6. How to use Cross Product
7. 7. Setup 1 - Rotating an Object around Another
8. 8. Setup 2 - Vector Fields
9. 9. Hint for the future, and Session Recap
1. 1. Introduction
2. 2. Gradient Vectors
3. 3. A Setup using Gradient Vectors
4. 4. Resources for these Topics
5. 5. Q&A: Gradient for a Sphere
6. 6. Divergence and Curl
1. 1. Class Introduction
2. 2. Why Do We Need Quaternions?
3. 3. Rotation Order Explained
4. 4. Gimbal Lock
5. 5. Interpolating Rotations
1. 1. Introduction
2. 2. Number Systems
3. 3. Intro to i
4. 4. The Complex Plane
5. 5. Rotating in the Complex Plane
6. 6. Rotating UVs in Houdini
7. 7.Rotating by Angles Other Than 90
8. 8. Q&A: Multiplying Negatives
9. 9. Expanding Complex Numbers to 4D
10. 10. What We Need to Use Quaternions
11. 11. Visualizing Axis and Angle
1. 1. Setup 1- Rotating Vectors on a Sphere
2. 2. What the Quaternion Func Does
3. 3. Setup 1 cont- Using qrotate
4. 4. Setup 2- Making Flippy Flap His Wings
5. 5. Recap of The pow Function
6. 6. Setup 2 cont.- Animating the Flapping
7. 7. Setup 3- Using The orient Attribute With Copy to Points
8. 8. Q&A: When to Use Quats
9. 9. Why We Use Vex to Manipulate Quats
1. 1. Dihedral
2. 2. Setup using Dihedral
3. 3. Fixing the normals
4. 4. Q&A: Rotating Attributes, Defining the Front Axis
5. 5. Interpolating Quaternions
6. 6. Q&A: Slerp and Shortest Distance
7. 7. Adding a Spring Motion to a Slerp
1. 1. Introduction to Layering Quats
2. 2. Multiplying Quaternions
3. 3. Chain Link
4. 4. Interlocking the Chain
5. 5. The Problem with Using Up and N
6. 6. Interlocking Using Orient
7. 7. Second Layer of Rotations
8. 8. Reversing Rotations Using Quat. Inverse
9. 9. Recap of the Rotations
10. 10. Q&A: Rotating before Creating orient
11. 11. Adding a Third Layer
12. 12. Winding Motion With curveu
13. 13. Last Thoughts on Quats
1. 1. Why Divy Loves Matrices
2. 2. Session Overview
3. 3. Correction to Session 2
4. 4. Transformation Order
5. 5. Transformation Order Part 2
6. 6. A Matrix from Basis Vectors
7. 7. Creating a Matrix in VEX
8. 8. Recap
1. 1. Determinants
2. 2. Inverse Matrices
3. 3. A Caveat with Inverse Matrices
4. 4. Recap
1. 1. Scaling with Matrices
2. 2. Matrix Multiplication
3. 3. Q&A: Converting Matrix Sizes
4. 4. Rotating with Matrices
5. 5. Rotating with a 2x2 Matrix
6. 6. Rotating on 3 Axes
7. 7. Why -Sin(Θ)?
8. 8. Important Concept
9. 9. Translating with Matrices
1. 1. Introduction
2. 2. Matrix Functions in VEX
3. 3. Q&A: Transformation Order
4. 4. Building a Matrix from Basis Vectors
5. 5. Recap
6. 6. Q&A: Rotating and Pivots
7. 7. Converting Cartesian to Polar Coordinates
8. 8. Spherical Coordinates
9. 9. Matrix Flowers
1. 1. Working with Packed Geo
2. 2. Interpolation
3. 3. Copy to Points
4. 4. Animating the Copy to Points
5. 5. Q&A: Morphing
6. 6. Recap
7. Submit your work

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.

Introduction
Number System
Brief Introduction to Complex Numbers
Introduction to Mathematical Functions
Algebra of Functions
Function composition
Use cases of some common functions
Cartesian Coordinates
Developing mindset for the transformation of space using Polar Coordinates
Linear Interpolation & Smooth Step
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.

Introduction to Vectors
Point Vs Direction
Magnitude & Direction of Vectors
Resolution of Vector
Algebra of Vectors
Dot Product
Cross Product
Vector Fields
Divergence & Curl
Gradient Vectors
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.

Introduction to Quaternions
Euler Angles Vs Quaternions
Relationship between Quaternions and Complex Numbers
3D Rotation using Quaternions
Euler Angles to Quaternions
Quaternions to Euler Angles
Quaternion to Rotation Matrix
Quaternion Interpolation
Other useful Quaternion Functions
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.

Introduction to Matrices
Matrix Multiplication
Unpacking the Matrix
Basis Vectors
Cylindrical & Spherical Coordinate Systems
Transformation using Matrices
Quaternions and Matrices
Matrix Interpolation
Use cases of Matrices in Computer Graphics
Recap

Instructor

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.

WHAT YOU NEED TO TAKE THIS COURSE

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

ADDITIONAL INFORMATION

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REFUND POLICY:

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:

Student’s full name
Name of the course(s) being dropped

Testimonials

“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!

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HS-223: Maths for Artists

Course Overview

Class Description:

Learning Outcomes:

Course curriculum

Resources

1. Introduction

2. Three Ways to Make a Circle

3. Basics of Functions

4. Making Masks

5. Polar Coordinates

6. Vectors 101

7. Vector Arithmetic

8. Dot Product

9. Cross Product

10. Bonus Topics

11. Introduction

12. Background on Quaternions

13. Using Quaternions

14. Other ways to use Quats

15. Layering Quaternions

16. Into the Matrix

17. Matrix Concepts

18. Understanding Transformations

19. Using Matrices in Houdini

20. More Matrix Topics