Intersection-Free and Topologically Faithful Slicing of Implicit Solid

Abstract

We present a robust and efficient approach to directly slicing implicit solids. Different from prior slicing techniques that reconstruct contours on the slicing plane by tracing the topology of intersected line segments, which is actually not robust, we generate contours by a topology guaranteed contour extraction on binary images sampled from given solids and a subsequent contour simplification algorithm which has the topology preserved and the geometric error controlled. The resultant contours are free of self-intersection, topologically faithful to the given r-regular solids and with shape error bounded. Therefore, correct objects can be fabricated from them by rapid prototyping. Moreover, since we do not need to generate the tessellated B-rep of given solids, the memory cost our approach is low—only the binary image and the finest contours on one particular slicing plane need to be stored in-core. Our method is general and can be applied to any implicit representations of solids.

Towards additive manufacturing oriented geometric modeling using implicit functions

“…It should be noted that while implicit modeling is AM-friendly, it is not a convenient form of subtractive Fig. 14 Implicit shape designed by blending an implicit geometry with a real world object reconstructed by using an implicit fitting technique manufacturing, where the boundary of a slice needs to be calculated, which is not a simple task when the internal support structure is relatively complicated [46].…”

From 3D models to 3D prints: an overview of the processing pipeline

“…The contours extracted from ray-reps have typically many small segments -each slice is an image and contours are extracted as the outline of the solid pixels. Huang et al [HWC13] describe a topology preserving contour simplification, and a full image based pipeline for additive manufacturing [HWC14]. Another difficulty is the large memory requirements, which is roughly proportional to the surface area.…”

Optimal Discrete Slicing

“…Geometric or topological features that cannot be represented on the grid could not have been manufactured, so the discrete representation causes no loss relative to the physical artifact to be manufactured. The reach [Federer 1959] (which has been aptly called local feature size in computational geometry [Amenta and Bern 1999]) can be used to relate features to the grid resolution and decide whether a feature could be represented on the grid [Huang et al 2013]. An important part of our implementation is that we never store the shape as a discrete binary grid in our implementation.…”

“…If we wanted to avoid topological problems resulting from slicing we could also assign E(x, y, z i , z j ) = ∞ when more than two intersections occur. As such slices are unavailable this would effectively avoid topological inconsistencies resulting from selecting thick slices: for none or one intersection our assignment is identical to the intersection with the mid-level of a slice, so the topology would be preserved (compare [Huang et al 2013]). We discuss the issue of geometric accuracy further by relating our approach, and slicing in general, to signal processing in Section 6.…”