Sampling from Quadric‐Based CSG Surfaces

Abstract

Figure 1: Our method takes a CSG object defined by quadric surfaces and computes a set of per-surface low-distortion parametrizations. On these, we perform an adaptive subdivision guided by a conservative distance function (left). Once all CSG surface patches are identified, we can generate point samples on them (middle). Our splat-based rendering guarantees perfect surface reconstruction (right). In this example, 327 000 samples across 80 quadric primitives were generated. For models of this complexity, we can generate about a million surface samples per second per CPU core. Render time is 0.5 ms at 1080p.

Contact detection between a small ellipsoid and another quadric

“…The described algorithms set the theoretical framework for a method to detect contact between a small ellipsoid and a model which is build upon a combination of quadrics. Future research should be oriented to study their application in more sophisticated CAD models, where methodologies such as constructive solid geometry based on quadrics (see Trettner and Kobbelt (2021)) or other methods to detect contact between quadrics (see, for example, Choi et al (2014)) can also be used.…”

Change Detection between Retrospective and Contemporary 3D Models of the Omega House at the Athenian Agora

“…In this work, CSG is applied on the Omega House models [12][13][14][15][16]32] to calculate the Boolean operations thatare named difference and intersection. CSG is a technique to define a complex surface as the result of several set operations on solid regions of space: union, intersection, set difference, symmetric difference, complement.…”

“…In this paper, we compare the two models using Constructive Solid Geometry (CSG) operations [11][12][13][14][15][16] for performing Boolean operations on the Omega House models; additionally, distance and volume calculations are performed. Omega House monument can show the way that natural processes affect an exposed archaeological site.…”