Parameterizing rational offset canal surfaces via rational contour curves

Bizzarri, Michal; Lávička, Miroslav

doi:10.1016/j.cad.2012.10.017

Cited by 13 publications

(18 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…And this is always satisfied for valid input data; see [26]. Consequently, the solution of the linear systems (24) and (25) gives the envelope surface x; see Fig. 7 (bottom, left).…”

Section: Re Surface Patches Interpolating Given Points With Boundariementioning

confidence: 87%

See 1 more Smart Citation

Skinning and blending with rational envelope surfaces

Bizzarri

Lvika

Kosinka

2017

Computer-Aided Design

Self Cite

View full text Add to dashboard Cite

We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain's boundary, i.e., the envelope of the corresponding 2-parameter family of spheres. We formulate efficient algorithms for G 1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations.

show abstract

“…And this is always satisfied for valid input data; see [26]. Consequently, the solution of the linear systems (24) and (25) gives the envelope surface x; see Fig. 7 (bottom, left).…”

Section: Re Surface Patches Interpolating Given Points With Boundariementioning

confidence: 87%

“…For constructing the blending shapes (ii) we can use e.g. the algorithm formulated in [25]. It is based on using rational contour curves of canal surfaces for computing their rational parametrizations.…”

Section: Skinning Balls In 3d Spacementioning

confidence: 99%

Skinning and blending with rational envelope surfaces

Bizzarri

Lvika

Kosinka

2017

Computer-Aided Design

Self Cite

View full text Add to dashboard Cite

show abstract

“…i.e., it is a closure of the image of the isophote s a; under normal mapping (3). Now, observe that that the normal mapping sends a generic ruling v & to the line.…”

Section: Isophotesmentioning

confidence: 95%

“…Hence for a given surface one would like to have a formula for a rational parameterization of its contours. Conversely in [3] the rational contour curves were used to produce rational parametrizations of canal surfaces. So the first question to ask is how many rational surfaces possesses rational contours.…”

Section: Contour Curves In Generalmentioning

confidence: 99%

“…with respect to a polarity induced by the absolute conic section . With the choice of we have made, the normal mapping is X p U 3 @@ x1 F @pA X ¡ ¡ ¡ X @ x3 F @pAA ; (3) i.e., it can be viewed as the composition of the Gauss mapping and the projection from the point @I X H X H X HA. It is easily verified that this definition agrees with the usual construction of the normal vector on the affine patch x 0 T a H.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Contour curves and isophotes on rational ruled surfaces

Vršek

2018

Computer Aided Geometric Design

View full text Add to dashboard Cite

The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the field of applied geometry. An isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some fixed vector. Choosing an angle equal to =2 we obtain a special instance of a isophotethe so called contour curve. While contours on rational ruled surfaces are rational curves, this is no longer true for the isophotes. Hence we will provide a formula for their genus. Moreover we will show that the only surfaces with a rational generic contour are just rational ruled surfaces and a one particular class of cubic surfaces. In addition we will deal with the reconstruction of ruled surfaces from their contours and silhouettes.

show abstract

Approximation of Implicit Blends by Canal Surfaces of Low Parameterization Degree

Bizzarri

Lávička

2014

Mathematical Methods for Curves and Surfaces

View full text Add to dashboard Cite

Parameterizing rational offset canal surfaces via rational contour curves

Cited by 13 publications

References 32 publications

Skinning and blending with rational envelope surfaces

Skinning and blending with rational envelope surfaces

Contour curves and isophotes on rational ruled surfaces

Approximation of Implicit Blends by Canal Surfaces of Low Parameterization Degree

Contact Info

Product

Resources

About