zoukankan      html  css  js  c++  java
  • 坐标的平移旋转

    平移:
    假设M是原点为(0,0,0)的坐标系,N是原点为(2,2,2)的坐标系,点P(px,py,pz)是M中的一点,那么点P在N中的坐标P‘是多少呢?
    p'x = px - 2;p'y = py - 2;p'z = pz - 2;换成矩阵看看:

    [java] view plaincopy
    1. p'x = |px| + |-2|  
    2. p'y = |py| + |-2|  
    3. p'z = |pz| + |-2|  

    换成齐次坐标就为:

    [java] view plaincopy
    1. |p'x|   | 1 0 0 tx|   |px|  
    2. |p'y| = | 0 1 0 ty| * |py|  
    3. |p'z|   | 0 0 1 tz|   |pz|  
    4. 1 |   | 0 0 0  1|   |1 |  

    对上面来讲:tx=-2,ty=-2;tz=-2;

    旋转:
    假设M是原点为(0,0,0)的坐标系,点p(px,py,pz)绕z轴逆时针旋转a度到点p',那么点p'是多少呢?
    p'x = px*cosa - py*sina
    p'y = px*sina + py*cosa
    p'z = z
    换成齐次坐标就为:

    [java] view plaincopy
    1. |x'|   |cosa -sina 0 0|   |x|  
    2. |y'| = |sina  cosa 0 0| * |y|  
    3. |z'|   |0      0   1 0|   |z|  
    4. |1 |   |0      0   0 1|   |1|  

    那么绕x轴呢?
    p'y = py*cosa - pz*sina
    p'z = py*sina + pz*cosa
    p'x = x
    换成齐次坐标就为:

    [java] view plaincopy
    1. |x'|   |1  0     0   0|   |x|  
    2. |y'| = |0 cosa -sina 0| * |y|  
    3. |z'|   |0 sina  cosa 0|   |z|  
    4. |1 |   |0  0     0   1|   |1|  

    那么绕y轴呢?
    p'z = pz*cosa - px*sina
    p'zx =pz*sina + px*cosa
    p'y = y
    换成齐次坐标就为:

    [java] view plaincopy
    1. |x'|   | cosa 0 sina 0|   |x|  
    2. |y'| = | 0    1  0   0| * |y|  
    3. |z'|   |-sina 0 cosa 0|   |z|  
    4. |1 |   | 0    0  0   1|   |1|  

    缩放:
    假设M是原点为(0,0,0)的坐标系,点P(px,py,pz)沿x轴缩放sx,沿y轴缩放sy,沿z轴缩放sz后的坐标p'是多少呢?
    p'x = px * sx
    p'y = py * sy
    p'z = pz * sz
    换成齐次坐标就为:

    [java] view plaincopy
    1. |x'|   |sx 0  0  0|   |x|  
    2. |y'| = |0  sy 0  0| * |y|  
    3. |z'|   |0  0  sz 0|   |z|  
    4. |1 |   |0  0  0  1|   |1|
  • 相关阅读:
    168. Excel Sheet Column Title
    171. Excel Sheet Column Number
    264. Ugly Number II java solutions
    152. Maximum Product Subarray java solutions
    309. Best Time to Buy and Sell Stock with Cooldown java solutions
    120. Triangle java solutions
    300. Longest Increasing Subsequence java solutions
    63. Unique Paths II java solutions
    221. Maximal Square java solutions
    279. Perfect Squares java solutions
  • 原文地址:https://www.cnblogs.com/zfluo/p/5131840.html
Copyright © 2011-2022 走看看