| R. C. Veltkamp, 3D computational morphology, Computer Graphics Forum (Proc. EUROGRAPHICS) (1993) 115--127. 2 |
....a parametric curve is called parametric continuity and denoted C n in the literature. Two intersecting parametric curves, r(u) and s(v) are C n continuous at their point of intersection, r(u o ) s(v o ) if and only if their nth derivatives evaluated at u o and v o respectively, are equal [31], i.e. d n r du n u = u o = d n s dv n v = v o (2) However, a given curve may have many different parametric representations which have different parametric continuity properties. A less restrictive definition of continuity, called geometric continuity and denoted G n for ....
Veltkamp, R.C., Survey of Continuities of Curves and Surfaces, Computer Graphics forum, Vol. 11(2), pp. 93-112, 1992.
....using parametric surfaces. However, these schemes cannot be used directly in the fitting of dense, noisy point sets obtained from range scanners. Two recent articles describing methods for fitting either piecewise linear or everywhere smooth surfaces of arbitrary topological type are Veltkamp [21] and Szeliski et al. 20] We are not aware of any methods for fitting piecewise smooth surface models of arbitrary topological type. 7 Summary and future work We have described a piecewise smooth surface reconstruction procedure that produces concise and accurate surface models from unorganized ....
R.C. Veltkamp. 3D computational morphology. Computer Graphics Forum, 12(3):116--127, 1993. 14
....a survey. These schemes are designed to interpolate sparse data, rather than to fit dense, noisy point sets of the type obtained from range scanners. Two recent articles describing methods for fitting either piecewise linear or everywhere smooth surfaces of arbitrary topological type are Veltkamp [27] and Szeliski et al. 26] We are not aware of any previous method for fitting piecewise smooth surface models of arbitrary topological type to dense, noisy data, although one could imagine developing such a procedure based on a piecewise smooth triangular patch method such as Nielson s ....
R.C. Veltkamp. 3D computational morphology. Computer Graphics Forum, 12(3):116--127, 1993.
....This paper introduces some design operators that do not suffer from this problem. The effect of such an operator is defined by an energy functional. Since this functional depends on properties from outside the surface, it is called external. This has been proved to be successful for 3D curves [Veltkamp and Wesselink, 95] and is extended to surfaces in this paper. We have tested these concepts in a prototype system for modeling surfaces of cubic triangular B ezier patches. Our external energy operators are more general for design than only spring forces (see e.g. Terzopoulos and Qin, 94] Other surface ....
R. C. Veltkamp and W. Wesselink. Modeling 3d curves of minimal energy. Computer Graphics Forum, 14(3), 1995, 97--110. Proceedings Eurographics'95.
....of representing curves is by their position function, de ning all the positions of the curve. A parametric curve A is de ned in terms of a parameter: A(t) x(t) y(t) In general, many parameterizations result in the same shape of the curve, but have di erent derivative vectors along the curve [Vel92] A standard parameterization is by arc length along the curve; the arc length is usually denoted by s. Polygonal curves (polylines) are usually represented by Figure 8: Polygonal curve and turning function. their sequence of vertices. An implicit de nition of the curve, A : f(x; y) 0, is ....
Remco C. Veltkamp. Survey of continuities of curves and surfaces. Computer Graphics Forum, 11(2):93-112, 1992.
No context found.
R. C. Veltkamp, 3D computational morphology, Computer Graphics Forum (Proc. EUROGRAPHICS) (1993) 115--127. 2
No context found.
Veltkamp R.C., Survey of Continuities of Curves and Surfaces, Computer Graphics Forum, Vol. II, No. 2, June 1992, 93--112.
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