Arcball轨迹球

Posted 2020-09-23 Reise

Arcball屏幕后面的虚拟轨迹球。Arcball的作用是输入屏幕上的点击或拖动，输出轨迹球的旋转量（旋转矩阵或四元数），用来控制摄像机等物体的旋转。

 https://en.wikibooks.org/wiki/OpenGL_Programming/Modern_OpenGL_Tutorial_Arcball

1. Convert the screen coordinates (in pixels) to camera coordinates (in [-1, 1])
2. Compute the vectors OP1 and OP2, the points at the surface of the ball that match our mouse click
   • x and y coordinates are directly taken from the click in camera coordinates
   • z coordinate is computed using the classical Pythagorean theorem
   • If P1 or P2 is too far away from the sphere (), we normalize it to get the nearest point on the surface of the ball
3. We have {\\displaystyle \\scriptstyle \\mathbf, and the ball\'s size is 1 (), so we get the angle using .
4. Get the rotation axis in 3D, we compute , which will give a unit perpendicular vector