Adaptive Implicit Surface Polygonization Using Marching Triangles

Abstract

This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crack‐closing method invoked at the end of the mesh growing step. Eventually, we show that the marching triangles can be used as an incremental meshing technique in an interactive modeling environment. In contrast to existing incremental techniques based on spatial subdvision, no extra data‐structure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.

Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

“…For each bisector half-plane we define two blending half-planes B l j 1 The curves are projected orthogonally in the plane with normal (∇ f )(v) through v, and then ordered clockwise. and B r j which include a user-specified small angle θ with B j and also contain the line (23).…”

“…If all these boundary edges are deleted, then continue with (1). If no such boundary edge did exist, then continue with (4).…”

“…In order to get a triangulation of the surface which preserves the features, we define the initial curve for this triangulation method as a polygon which has been sampled from the edge curves. See also [1,37] for more advanced polygonization techniques for implicit defined objects. We apply the sharp triangle detection to the triangular mesh of the initial surface.…”

A Calligraphic Interface for Interactive Free-Form Modeling with Large Datasets

“…In this vein, FreeFormSKETCH improves on our previous surface-tracking algorithm [7] by taking advantage of MPU implicits, offering support for sharp fea- tures and, most importantly, local re-polygonization. Previously, Akkouche [2] presented a technique for adaptive meshing of implicit functions, based on Marching Triangles [1], a surface tracking algorithm. However, his method performs polygonization using two steps.…”

High-quality tree structures modelling using local convolution surface approximation

“…Furthermore, it is prone to missing small twigs for complex tree models because the output of the Marching cubes is resolutiondependent. Even though there are a large number of improvements [55,8,10,1,40,59], it is still difficult to balance the quality of the iso-surface polygons and the performance. To solve these problems, we propose an interactive GPU-based quad-only tessellation method to polygonize convolution surfaces with good edge flows along the skeletons of tree models.…”