Polygonization of Implicit Surfaces With Constructive Solid Geometry

Wyvill, Brian; Overveld, Kees van

doi:10.1142/s0218654396000142

Cited by 19 publications

(10 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, Bloomenthal and Ferguson [BF95] extract non-manifold isosurfaces produced from trimming implicits and parameterics using a tetrahedral isosurface algorithm. [WvO96] polygonize boolean combinations of skeletal implicits (Boolean Compound Soft Objects), applying an iterative solver and face subdivision for placing vertices along feature edges and points. Suffern and Balsys [SB03] present an algorithm to polygonize surfaces defined by two implicit functions provided in analytic form; this same algorithm can compute bi-iso-lines of pairs of implicits for rendering.…”

Section: Marching Tetrahedramentioning

confidence: 99%

3D scanning for personal 3D printing

Taubin

Moreno

Lanman³

2014

ACM SIGGRAPH 2014 Studio

View full text Add to dashboard Cite

3D Printing has entered the mainstream. Multiple low cost desktop 3D printers are currently available from various vendors, and open source projects let hobbyists build their own. This course addresses the problem of creating 3D models for 3D printing. As is the case for 3D printers, low-cost homemade 3D scanners are now within reach of students and hobbyists with a modest budget. This course provides the students with the necessary mathematics, software, and practical details to leverage projector-camera systems to build their own desktop 3D scanner. An exampledriven approach is used throughout, with each new concept illustrated using a practical scanner implemented with off-the-shelf parts. First, the mathematics of triangulation is explained using the intersection of parametric and implicit representations of lines and planes in 3D. The particular case of ray-plane triangulation is illustrated using a scanner built with a single camera and a modified laser pointer. Camera calibration is explained at this stage to convert image measurements to geometric quantities. The mathematics of rigid-body transformations are covered through this example. Next, the details of projector calibration are explained through the development of a classic structured light scanning system using a single camera and projector pair. A minimal postprocessing pipeline is described to convert the point-based representations produced by these scanners to watertight meshes. Key topics covered in this section include: surface representations, file formats, data structures, polygonal meshes, and basic smoothing and gap-filling operations. The course concludes with the description of some commercially available low cost desktop 3D scanners. PrerequisitesAttendees should have a basic undergraduate-level understanding of linear algebra. While executables are provided for beginners, attendees with prior knowledge of Matlab, C/C++, and Java programming will be able to directly examine and modify the provided source code.i he won a Fulbright Specialist grant. He has authored numerous reviewed book chapters, journal, or conference papers, and is a co-inventor of 48 international patents. He has made significant theoretical and practical contributions to the field now called Digital Geometry Processing, comprising: 3D shape capturing and surface reconstruction, geometric modeling, geometry compression, progressive transmission, signal processing, and display of discrete surfaces. He teaches courses on 3D Photography and Digital Geometry Processing at Brown University on a regular basis. Daniel MorenoBrown University, daniel moreno@brown.edu Daniel A. Moreno received a degree of Licenciado en Ciencias de la Computacion from Universidad Nacional de Rosario, Argentina, in 2011. The same year, he joined Brown University where he is currently pursuing a PhD in Engineering. His research topic is Computer Vision, specifically the area of 3D models acquisition and processing. Recently, he has been working on structuredlight systems calibration and low-cost ...

show abstract

Section: Marching Tetrahedramentioning

confidence: 99%

3D scanning for personal 3D printing

Taubin

Moreno

Lanman³

2014

ACM SIGGRAPH 2014 Studio

View full text Add to dashboard Cite

show abstract

“…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.…”

Section: Edge Curve Fitting and Triangulationmentioning

confidence: 99%

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

Song

Jüttler

2009

Computers & Graphics

View full text Add to dashboard Cite

We propose a new method for describing sharp features (i.e., edges and vertices) of implicitly defined surfaces. We consider an initial implicitly defined surface, which is represented as the zero set of a C 1 smooth scalar field with non-vanishing gradients. In order to represent sharp edges and vertices, this surface is augmented by adding new types of implicit representations, called edge descriptors and vertex descriptors. They are defined with the help of the distance field of edge curves. In our implementation, we use circular splines to describe these edge curves, since they support a fast and non-iterative closest point computation.After adding the edge and vertex descriptors to the initial scalar field, the zero set of the augmented function contains the sharp features. We apply the new representation to surface modelling by implicitly defined surfaces with sharp features and to object reconstruction. In the latter case we describe an algorithm for detecting the sharp curves and vertices of a shape which is given by an unorganized point cloud, which are then approximated by circular splines, in order to define the edge and vertex descriptors.

show abstract

“…The major advantage of implicit surface modeling systems has been the use of automatic blending between skeletal elements. Recent developments in such systems include the addition of Boolean operations reminiscent of CSG systems 1 and space warping which provides a method of implementing deformations 2,3 .…”

Section: Introductionmentioning

confidence: 99%

Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System

Wyvill

Guy

Galin

1999

Computer Graphics Forum

Self Cite

203

176

View full text Add to dashboard Cite

Automatic blending has characterized the major advantage of implicit surface modeling systems. Recently, the introduction of deformations based on space warping and Boolean operations between primitives has increased the usefulness of such systems. We propose a further enhancement which will extend the range of models that can be easily and intuitively defined with a skeletal implicit surface system. We describe a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and Boolean operations. We call this structure the BlobTree. Blending and space warping are treated in the same way as union, difference and intersection, i.e. as nodes in the BlobTree. The traversal of the BlobTree is described along with two rendering algorithms; a polygonizer and a ray tracer. We present some examples of interesting models which can be made easily using our approach that would be very difficult to represent with conventional systems.

show abstract

Polygonization of Implicit Surfaces With Constructive Solid Geometry

Cited by 19 publications

References 12 publications

3D scanning for personal 3D printing

3D scanning for personal 3D printing

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

Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System

Contact Info

Product

Resources

About