A general construction scheme for unit quaternion curves with simple high order derivatives
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Unit quaternion integral curve: a new type of fair free-form curves
Computer Aided Geometric Design
Consistent mesh parameterizations
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Metamorphosis of Arbitrary Triangular Meshes
IEEE Computer Graphics and Applications
A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations
CA '95 Proceedings of the Computer Animation
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Domain decomposition for multiresolution analysis
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Multiresolution Interpolation Meshes
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
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In this paper, we propose a method for creating parametric curves on triangular meshes. A curve on a mesh is frequently used as a boundary curve of a specific region of a mesh in mesh modeling and applications such as texture mapping, remeshing or morphing. Although the curve defined in this paper is a piecewise linear approximation of a strict parametric curve, it is guaranteed that such a curve is just on a mesh. The basic idea is creating a curve on a spherical parameterization instead of direct definition on a mesh. The computation of this curve is done by using only the control points on a spherical parameterization which does not depend on the number of vertices in a mesh. This enables interactive creation/modification of curves even for dense meshes.