Department of Computer Science and Technology

Technical reports

Rendering for free form deformations

Uwe Michael Nimscheck

October 1995, 151 pages

This technical report is based on a dissertation submitted by the author for the degree of Doctor of Philosophy to the University of Cambridge, Wolfson College.



Sederberg’s Free Form Deformation (FFD) is an intuitive modelling technique that lets users sculpt and deform objects without having to worry about internal model representation issues. Unfortunately displaying these deformed objects is problematic and there exist no algorithms to display general FFD deformed polygonal models. Based on deRose’s Bezier composition algorithms we develop geometrically intuitive composition algorithms to find analytic expressions for deformed objects, which can then be rendered using standard rendering hardware. Alternatively, one can adaptively tessellate deformed objects into a mesh of triangles and display this deformed mesh. The finite element method provides us with a wealth of algorithms to mesh all types of objects. We show how to adapt these algorithms to computer graphics problems. The main problem is to define curvature measures to vary the mesh density according to the curvature of deformed objects. We find such measures and use them to develop a new meshing scheme, based on Lo’s advancing front algorithm, to mesh and render FFD deformed objects. Our algorithm is superior to existing schemes both in the quality of the generated meshes and in the variety of solids it can be applied to.

The major contributions of this dissertation are: Firstly, the development of geometrically intuitive algorithms to determine closed form expressions of FFD deformed surfaces. Secondly, the transformation of tangent and normal vectors into deformed space. Thirdly, development of a new advancing front meshing algorithm that allows to mesh solids that have been deformed by non-uniform B-spline volumes. Finally, systematic experiments have been performed to assess the performance and limitations of the new meshing algorithm.

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BibTeX record

  author =	 {Nimscheck, Uwe Michael},
  title = 	 {{Rendering for free form deformations}},
  year = 	 1995,
  month = 	 oct,
  url = 	 {},
  institution =  {University of Cambridge, Computer Laboratory},
  doi = 	 {10.48456/tr-381},
  number = 	 {UCAM-CL-TR-381}