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CatmullClark subdivision surface 30
References
[1] E. Catmull and J. Clark: Recursively generated B-spline surfaces on arbitrary topological meshes, Computer-Aided Design 10(6):350-355
(November 1978), ( doi (http:/ / dx. doi. org/ 10. 1016/ 0010-4485(78)90110-0), pdf (http:/ / www. idi. ntnu. no/ ~fredrior/ files/
Catmull-Clark 1978 Recursively generated surfaces. pdf))
[2] Jos Stam, Exact Evaluation of Catmull–Clark Subdivision Surfaces at Arbitrary Parameter Values, Proceedings of SIGGRAPH'98. In
Computer Graphics Proceedings, ACM SIGGRAPH, 1998, 395–404 ( pdf (http:/ / www. dgp. toronto. edu/ people/ stam/ reality/ Research/
pdf/ sig98. pdf), downloadable eigenstructures (http:/ / www. dgp. toronto. edu/ ~stam/ reality/ Research/ SubdivEval/ index. html))
Conversion between quaternions and Euler
angles
Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article
explains how to convert between the two representations. Actually this simple use of "quaternions" was first
presented by Euler some seventy years earlier than Hamilton to solve the problem of magic squares. For this reason
the dynamics community commonly refers to quaternions in this application as "Euler parameters".
Definition
A unit quaternion can be described as:
We can associate a quaternion with a rotation around an axis by the following expression
where α is a simple rotation angle (the value in radians of the angle of rotation) and cos(β x ), cos(β y ) and cos(β z ) are
the "direction cosines" locating the axis of rotation (Euler's Theorem).