Arcball轨迹球

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{\displaystyle \scriptstyle b\;=\;{\sqrt {c^{2}\,-\,a^{2}}}.\,}
    • If P1 or P2 is too far away from the sphere ({\displaystyle \scriptstyle \left|\mathbf {OP} \right|\;>\;1}), we normalize it to get the nearest point on the surface of the ball
  3. We have {\displaystyle \scriptstyle \mathbf{\displaystyle \scriptstyle \mathbf {a} \cdot \mathbf {b} \;=\;\left\|\mathbf {a} \right\|\,\left\|\mathbf {b} \right\|\cos(\theta )}, and the ball's size is 1 ({\displaystyle \scriptstyle \left\|\mathbf {a} \right\|\;=\;\left\|\mathbf {b} \right\|\;=\;1}), so we get the angle using {\displaystyle \scriptstyle \arccos \left(\mathbf {OP1} \cdot \mathbf {OP2} \right)}.
  4. Get the rotation axis in 3D, we compute {\displaystyle \scriptstyle \mathbf {OP1} \times \mathbf {OP2} }, which will give a unit perpendicular vector
posted @ 2017-06-20 23:53  Reise  阅读(522)  评论(0)  编辑  收藏  举报