TY - JOUR

T1 - Reuse of B-spline-based shape interrogation tools for triangular mesh models

AU - Kobashi, Yuji

AU - Suzuki, Junya

AU - Joo, Han Kyul

AU - Maekawa, Takashi

PY - 2012/1/1

Y1 - 2012/1/1

N2 - In many engineering applications, a smooth surface is often approximated by a mesh of polygons. In a number of downstream applications, it is frequently necessary to estimate the differential invariant properties of the underlying smooth surfaces of the mesh. Such applications include first-order surface interrogation methods that entail the use of isophotes, reflection lines, and highlight lines, and second-order surface interrogation methods such as the computation of geodesics, geodesic offsets, lines of curvature, and detection of umbilics. However, we are not able to directly apply these tools that were developed for B-spline surfaces to tessellated surfaces. This article describes a unifying technique that enables us to use the shape interrogation tools developed for B-spline surface on objects represented by triangular meshes. First, the region of interest of a given triangular mesh is transformed into a graph function (z=h(x,y)) so that we can treat the triangular domain within the rectangular domain. Each triangular mesh is then converted into a cubic graph triangular Bézier patch so that the positions as well as the derivatives of the surface can be evaluated for any given point (x,y) in the domain. A number of illustrative examples are given that show the effectiveness of our algorithm.[Figure not available: see fulltext.]

AB - In many engineering applications, a smooth surface is often approximated by a mesh of polygons. In a number of downstream applications, it is frequently necessary to estimate the differential invariant properties of the underlying smooth surfaces of the mesh. Such applications include first-order surface interrogation methods that entail the use of isophotes, reflection lines, and highlight lines, and second-order surface interrogation methods such as the computation of geodesics, geodesic offsets, lines of curvature, and detection of umbilics. However, we are not able to directly apply these tools that were developed for B-spline surfaces to tessellated surfaces. This article describes a unifying technique that enables us to use the shape interrogation tools developed for B-spline surface on objects represented by triangular meshes. First, the region of interest of a given triangular mesh is transformed into a graph function (z=h(x,y)) so that we can treat the triangular domain within the rectangular domain. Each triangular mesh is then converted into a cubic graph triangular Bézier patch so that the positions as well as the derivatives of the surface can be evaluated for any given point (x,y) in the domain. A number of illustrative examples are given that show the effectiveness of our algorithm.[Figure not available: see fulltext.]

KW - B-spline surface

KW - PN triangles

KW - Shape interrogation

KW - Triangular mesh

UR - http://www.scopus.com/inward/record.url?scp=84874402360&partnerID=8YFLogxK

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U2 - 10.1007/3DRes.02(2012)4

DO - 10.1007/3DRes.02(2012)4

M3 - Article

AN - SCOPUS:84874402360

VL - 3

SP - 1

EP - 15

JO - 3D Research

JF - 3D Research

SN - 2092-6731

IS - 2

M1 - 4

ER -