Ray Tracing Multiple Minkowski Sums: a Csg Approach
نویسنده
چکیده
The repertoire of set operators available in Constructive Solid Geometry (CSG) may be extended by the Minkowski addition and subtraction operators. In this way the problem of visualizing 3D solids deened as a Minkowski addition or subtraction of elementary objects can be solved by using CSG in combination with ray tracing. The method consists in transforming a Minkowski term with multiple operands into a union of simple objects which can be handled by a standard ray tracer. Applications of the method are found in solid modeling and shape description.
منابع مشابه
Minkowski Sums of Set-theoretic Models
This paper describes a new algorithm for computing Min-kowski sums of set-theoretic geometric models. The algorithm uses a variation on Woodwark's method for feature recognition. At the end of the paper we present results from an implementation of the algorithm running on two-dimensional data, and from a more experimental version ray-tracing into three-dimensional Minkowski sums to render a pic...
متن کاملSpatially Efficient Tree Layout for GPU Ray-tracing of Constructive Solid Geometry Scenes
A novel GPU-optimized CSG ray-tracing approach is presented that is fast and accurate, and allows achieving real-time frame rates at full-screen resolutions. It has no limitations on the maximum number of primitives, and produces final image in a single pass. We propose an efficient procedure to transform an input CSG tree into equivalent spatially coherent and well-balanced form. Through vario...
متن کاملCSG Operations of Arbitrary Primitives with Interval Arithmetic and Real-Time Ray Tracing
We present a new method for interactively ray tracing constructive solid geometry (CSG) objects of arbitrary primitives represented as implicit functions. Whereas modeling globally with implicit surfaces suffers from a lack of control, implicits are well-suited for arbitrary primitives and can be combined through various operations. The conventional way to represent union and intersection with ...
متن کاملRay Tracing Implicit Surfaces
This is an overview of methods for ray tracing implicit surfaces, including the primary problem of intersecting a ray with an implicit surface, and the secondary problems of determining surface normals, and incorporating CSG operations and deformations.
متن کاملRay Tracing of Nonlinear Fractals
We present a new kind of parametric Lindenmayer-systems called nonlinear CSG-pL-Systems, which are useful for the modeling of nonlinear fractals and fractal like objects. Nonlinear CSGpL-systems describe cyclic CSG-Graphs, which can include several nonlinear transformations. To render the given objects a ray tracing algorithm is introduced, that is independent of the transformations and the und...
متن کامل