The SQuad data structure represents the connectivity of a triangle mesh by its “S table” of about 2 rpt (integer references per triangle). Yet it allows for a simple implementation of expected constant-time, random-access operators for traversing the mesh, including in-order traversal of the triangles incident upon a vertex. SQuad is more compact than the Corner Table (CT), which stores 6 rpt, ...

Most of the previous multiresolution models use exclusively the triangle graphic primitive both in the data structure and in the rendering stage. Only a few models use another graphic primitive in this rendering process and just one uses the triangle fan as the basic primitive of the model. In this paper we present the first multiresolution model, Multiresolution Triangle Strips, that uses the ...

Given a triangle center we can draw line segments from each vertex through the triangle center to the opposite side, this splits the triangle into six smaller triangles called daughters. Consider the following problem: Given a triangle S and a rule for finding a center find a triangle T , if possible, so that one of the daughters of T , when using the rule is S. We look at this problem for the ...

Is it possible that the lengths of two sides of a primitive Heron triangle have a c ommon factor? The triangle with sides 9, 65, 70 and area 252 shows that this is possible. But notice that the common factor 5 is a prime of the form 4+1. Surprisingly, however, such a common factor cannot be a prime of the form 4 ; 1. Heron's name is familiar to anyone who has used the formula = p s(s ; a)(s ; b...

A heptagonal triangle is a non-isosceles triangle formed by three vertices of a regular heptagon. Its angles are π 7 , 2π 7 and 4π 7 . As such, there is a unique choice of a companion heptagonal triangle formed by three of the remaining four vertices. Given a heptagonal triangle, we display a number of interesting companion pairs of heptagonal triangles on its nine-point circle and Brocard circ...

Consider a triangle whose three vertices are grid points. Let k denote the number of grid points in the triangle. We describe an indexing of the triangle: a bijective mapping from f0;. .. ; k ?1g to the grid points in the triangle. Computing such a mapping is a fundamental subroutine in ne-grained parallel computation arising in graphics applications such as ray-tracing. We describe a very fast...

In this paper two improvements to speed up collision detection are described. Firstly, a method called oncollide sphere-tree, OCST for short, is presented. This approach works by detecting collisions among models with arbitrary geometry using the video card’s Graphics Processing Units, GPU. While candidate parts of colliding objects are being detected, the OCST is constructed for collision eval...

Triangles meshes are the most popular standard model used to represent polygonal surfaces in Computer Graphics. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphic engine. The use of primitives such as triangle fans and strips, which make use of the connectivity information between the triangles in the mesh, dramatically reduces th...