將偏航和俯仰組合在一起

Question

爲什麼不導致相等的resultB？我不知道我在做什麼錯。你能給我一個解釋嗎？

float alpha = glm::radians(45.0f); 

glm::mat4 xRot(glm::vec4(1, 0, 0, 0), 
       glm::vec4(0, glm::cos(alpha), glm::sin(alpha), 0), 
       glm::vec4(0, -glm::sin(alpha), glm::cos(alpha), 0), 
       glm::vec4(0, 0, 0, 1)); 

glm::mat4 yRot(glm::vec4(glm::cos(alpha), 0, -glm::sin(alpha), 0), 
       glm::vec4(0, 1, 0, 0), 
       glm::vec4(glm::sin(alpha), 0, glm::cos(alpha), 0), 
       glm::vec4(0, 0, 0, 1)); 

glm::vec4 vec(0, 0, -100, 1); 

glm::vec4 resultA(0.0f); 
glm::vec4 resultB(0.0f); 

resultA = xRot * yRot * vec; //(-70.7107, 50, -50, 1) 
resultB = yRot * xRot * vec; //(-50, 70.7107, -50, 1) 

Answer 1

三維旋轉一般不通勤，除非是非常特殊的情況。因此：

xRot * yRot != yRot * xRot 

本質上講你與上面做的是證明了點:)

在這裏看到：http://en.wikipedia.org/wiki/Commutative_property