Last Lecture

  • What is Computer Graphics?
  • Why study Computer Graphics?
  • Course Topics
  • Course Logistics

Graphics’s Dependencies

  • Basic mathematics
    • Liner algebra, calculus, statistics.
  • Basic physics
    • Optics, Mechanics
  • Misc
    • Signal processing
    • Numerical analysis

线性代数

Dot(scalar) Product

Cross (vector) Product

向量之间的乘积不符合交换定律。

Cross product: Properties

右手螺旋定则

Cross product: Cartesian Formula

Cross product in Graphics

  • 判断左右
  • 判断内外
  1. 判断向量b在向量a的左边
    • 右手螺旋法则
    • 向量a x 向量b = + z
    • 向量a 顺时针旋转 到向量 b。所以向量b在向量a的左侧
  2. 点p在三角形的内部
    • 向量AB x 向量 AP = + z
    • 向量BC x 向量 BP = + z
    • 向量CA x 向量 CP = + z
    • 由此得出结论，p点在向量AB，向量BC，向量CA的左侧，所以p点在三角形内部

Orthonormal Coordinate Frames

Lecture3: Transformation

矩阵(matrix)

What is the matrix

Matrix-matrix Multiplication

Scale(Non-uniform)

Reflection Matrix

Shear Matrix

Rotate (about the origin(0,0) CCW by default)

Linear Transform = Matrix

Solution: Homogenous Coordinate

Homogenous Coordinate

Affine Transformations

Summary 2D Transformations

Composite Transform

3D Transform

3D Rotation

Lecture4: Transformation Cont

View/Camera Transformation

相机不会移动，都是在原点(0,0,0) 向-z看。

Perspective Projection(需要二刷)

Lecture 5: Rasterization 1 (Triangles)

--完--