CS 445: Topics for Sept 11/13/15, 2017

• Labs:

  • Complete: Lab 2: Getting Started with WebGL
  • Begin: Lab 3: Transformations
• Overview

  • Transformations are used for many tasks in computer graphics as can be seen in the rendering pipeline:

    

  • So far, we have seen how to create a variety of primitive shapes positioned in some cannonical location, size and orientation (e.g. around the origin, aligned with coordinate axes). We call this the Local or Object or Model Coordinates.

  • However, when we are creating a more interesting scene, we want these shapes to be positioned at various locations, sizes, and orientations in the scene (World Coordinates).

  • It turns out that there is no need to create a different cube for every possible situation. Instead, we use the cannonical cube we already created in Model Coordinates, and transform the cube to wherever we want it to be in the World Coordinates.

  • In the current lecture and lab, we will examine Modeling Transformations, which transform vertices from Model Coordinates to World Coordinates shown in red above.

• Resources
  • See Model Transform
  class handouts and notes

• Basic Geometric Transformations

  • Scalars, points, vectors, and their operations
  • What is a matrix equation.
  • Matrix and Vector operations and properties: addition, subtraction, determinants, dot product, cross product

  • 2D Transformations:

    • Translation, Scaling, Rotation, Reflection, Projection
    • Matrix representatons and homogeneous coordinates
    • Matrix operations and properties: identity, inverse, determinants
    • Matrix-Matrix and Matrix-point/vector operations
    • Inverse Transformations
    • Composition of Transformations
    • Rotation/Scaling about a Point

  • 3D Transformations:

    • Translation, Scaling, Reflection, Projection
    • Rotations: around each axis, around a specific axis
    • Matrix representatons and homogeneous coordinates
    • Inverse Transformations
    • Composition of Transformations
    • Rotation/Scaling about a Point
    • Euler Rotations and Gimbal Lock Explained and Euler (gimbal lock) Explained
    • Quaternion Rotations

• Scene Graphs

• Practice problems

• Look at Lab 3: Transformations to see how these are used in WebGL.