منابع مشابه
On convex Bézier triangles
— Goodman [8] showed that uniform subdivision of triangular Bézier nets preserves convexity. Hère, a very short proofofthis f act is given which applies even to box spline surfaces and degree élévation instead of subdivision. Secondiy, it is shown that every Bézier net of a quadratic convex Bézier triangle can be subdivided such that the net becomes convex.
متن کاملBézier Triangles with G2 Continuity across Boundaries
PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G0 continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and blend the corresponding Bézier triangles using a univariate blending function formulated in terms of barycentric coordinates. This produces G2 continu...
متن کاملOn Isosceles Triangles and Related Problems in a Convex Polygon
Given any convex n-gon, in this article, we: (i) prove that its vertices can form at most n2/2 + Θ(n log n) isosceles trianges with two sides of unit length and show that this bound is optimal in the first order, (ii) conjecture that its vertices can form at most 3n2/4 + o(n2) isosceles triangles and prove this conjecture for a special group of convex n-gons, (iii) prove that its vertices can f...
متن کاملMaximal Area Triangles in a Convex Polygon
In [12], the widely known linear time algorithm for computing the maximum area triangle in a convex polygon was found incorrect, and whether it can still be solved in linear time was proposed as an open problem. We resolved it affirmatively by presenting a new linear time algorithm. Our algorithm is simple and easy to implement, and it computes all the locally maximal triangles. 1998 ACM Subjec...
متن کاملSubharmonicity and convexity properties of Bernstein polynomials and Bézier nets on triangles
This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order to better compare these properties, the different notations used by different authors are unified. It also includes counterexamples for the results that are not true. 1999 Elsevier Science B.V. Al...
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ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 1992
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/1992260100231