圖形學基礎(2)

    http://blog.csdn.net/luckheadline

      最近的網速超級不穩定，導致我幾次寫得好好的結果都丟失了，憤怒ing。第二課其實也沒很多新鮮東西，主要是些線性代數等圖形學將用到的數學知識。我也不詳細去擴展了，很多都是高中和本科線性代數的內容。
three notation: scalar, vector, matrix
1. vector
(1)arrow: length+direction
(2)column vector vs row vector
(3)vector + vector = vector, parallelogram rule
(4)scalar * vector = vector
(5)dot product: inner product, vector * vector = scalar; u * v = |u||v|cosA
(6)cross product: vector × vector = vector; |u × v| = |u||v|sinA

2. line
(1)slope-intercept form: y = mx + b
(2)implicit form: y - mx - b = 0; Ax + By + C = 0; f(x, y) = 0;

3. circle
f(x, y) = (x - xc)*(x - xc) + (y - yc)*(y - yc) - r * r = 0

4. parametric curves
(1)2D parametric line
x = x0 + t(x1 - x0), y = y0 + t(y1 - y0);
p(t) = p0 + t(p1 - p0);
p(t) = o + t(d)

5. Matrix
(1)matrix + matrix = matrix
(2)scalar * matrix = matrix
(3)AB != BA
(4)p' = Mp; p'的轉置 = p的轉置 × M的轉置
(5)transpose
(6)identity
(7)inverse: not all matrix are invertible

6. Matrix and linear systems
(1)linear system of n equations, n unknowns
(2)matrix form Ax = b