Showing papers in "The Visual Computer in 1994"

A modified look-up table for implicit disambiguation of Marching Cubes

Abstract: A new triangulation scheme for the Marching Cubes algorithm is proposed. The scheme allows the extraction of continuous isosurfaces from volumetric data without the need to use disamgiguation techniques.

On generating topologically consistent isosurfaces from uniform samples

Abstract: A set of sample points of a function of three variables may be visualized by defining an interpolating functionf of the samples and examining isosurfaces of the formf(x, y, z)=t for various values oft. To display the isosurfaces on a graphics device, it is desirable to approximate them with piecewise triangular surfaces that (a) are geometrically good approximations, (b) are topologically consistent, and (c) consist of a small number of triangles. By topologically consistent we mean that the topology of the piecewise triangular surface matches that of the surfacef(x, y, z)=t, i.e., the interpolantf determines both the geometry and the topology of the piecewise triangular surface. In this paper we provide an efficient algorithm for the case in whichf is the piecewise trilinear interpolant; for this case existing methods fail to satisfy all three of the above conditions simultaneously.

Proximity clouds—an acceleration technique for 3D grid traversal

Abstract: In this paper we present a new method for the acceleration of ray traversal through a regular 3D grid. A distance transformation is precomputed and mapped onto the empty grid space. A ray traversing the empty space is assisted by the distance values which permit it to perform long skips along the ray direction. We show that the City-Block metric simplifies the preprocessing with no penalty at the traversal phase. Different schemes are discussed and the trade-off between the preprocessing time and the speed-up is analyzed.

Space-efficient region filling in raster graphics

Abstract: This paper presents fill algorithms for boundary-defined regions in raster graphics. The algorithms require only a constant-size working memory. The methods presented are based on the so-called “seed fill” algorithms that use the internal connectivity of the region with a given inner point. Basic methods, as well as additional hcuristics for speeding up the algorithm, are described and verified. Empirical results are used to compare the time complexities of the algorithms for different classes of regions.

Interrogation of differential geometry properties for design and manufacture

Abstract: This paper describes a new robust method to decompose a free-form surface into regions with specific range of curvature and provide important tools for surface analysis, tool-path generation, and tool-size selection for numerically controlled machining, tessellation of trimmed patches for surface interrogation and finite-element meshing, and fairing of free-form surfaces. The key element in these techniques is the computation ofall real roots within a finite box of systems of nonlinear equations involving polynomials and square roots of polynomials. The free-form surfaces are bivariate polynomial functions, but the analytical expressions of their principal curvatures involve polynomials and square roots of polynomials. Key components are the reduction of the problems into solutions of systems of polynomial equations of higher dimensionality through the introduction ofauxiliary variables and the use ofrounded interval arithmetic in the context of Bernstein subdivision to enhance the robustness of floating-point implementation. Examples are given that illustrate our techniques.

Computational morphology of curves

Abstract: We prove that euclidean minimal spanning trees correctly reconstruct differentiable arcs from sufficiently dense samples. The proof is based on a combinatorial characterization of minimal spanning paths and on a description of the local geometry of ares inside tubular neighborhoods. We also present simple heuristics for reconstruting more general curves.

Drawing with constraints

Abstract: The success of constraint-based approaches to drawing has been limited by difficulty in creating constraints, solving them, and presenting them to users. In this paper, we discuss techniques used in theBriar drawing program to address all of these issues. Briar's approach separates the problem of initially establishing constraints from the problem of maintaining them during subsequent editing. We describe how non-constraint-based drawing tools can be augmented to specify constraints in addition to positions. These constraints are then maintained as the user drags the model, which allows the user to explore configurations consistent with the constraints. Visual methods are provided for displaying and editing the constraints.

Solid sweeping in image space—application in NC simulation

Abstract: Displaying the result of sweeping a solid is usually accomplished by first evaluating the boundaries of the solid being swept out, and a standard shading method is then applied to obtain a realistic image of the solid. This paper present an algorithm for sweeping a 3D object in image space. The result obtained is another solid in image space. Boolean operations can then be performed on this model. By subtracting the swept-out solid from another solid, the proposed method can be used for simulating the material removal process in an NC machining operation.

Displacement constraints for interactive modeling and animation of articulated structures

Abstract: This paper presents an integrated set of methods for the automatic construction and interactive animation of solid systems that satisfy specified geometric constraints. Displacement contraints enable the user to design articulated bodies with various degrees of freedom in rotation or in translation at highes and to restrict the scope of the movement at will. The graph of constrained objects may contain closed loops. The animation is achieved by decoupling the free motion of each solid component from the action of the constraints. We do this with iterative tunings in displacements. The method is currently implemented in a dynamically based animation system and takes the physical parameters into account while reestablishing the constraints. In particular, first-order momenta are preserved during this process. The approach would be easy to extend to modeling systems or animation modules without a physical model just by allowing the user to control more parameters. (source Springer)

Modeling and animation of facial expressions based on B-Splines

Abstract: This paper describes a technique for the automatic adaptation of a canonical facial model to data obtained by a 3D laser scanner. The facial model is a B-spline surface with 13×16 control points. We introduce a technique by which this canonical model is fit to the scanned data and that takes into consideration the requirements for the animation of facial expressions. The animation of facial expressions is based on the facial action coding system (FACS). Using B-splines in combination with FACS, we automatically create the impression of a moving skin. To increase the realism of the animation we map textural information onto the B-spline surface.

A heuristic triangulation algorithm for multiple planar contours using an extended double branching procedure

Abstract: This paper presents a heuristic triangulation algorithm for reconstructing surfaces over a set of cross-sectional contours. The multiple branching problem, an important problem of conventional triangulation methods, is reated as a set of double branchings, and an algorithm based on countour merging is developed. Several imaginary contours are generated to handle the multiple branching problem with many branch contours. A double branching algorithm based on the partitioning of the root contour is also proposed. The results show that our method works well even for objects with many complicated branches.

Solid spaces and inverse particle systems for controlling the animation of gases and fluids

Abstract: This paper describes a new system for controlling the animation of gases, liquids, and volume density functions. This system is extremely powerful and flexible. It allows for the control of animation effects ranging from physically based motion of gases to the choreographed motion of gases. These techniques make extensive use of three-dimensional tables, including both flow vectors and motion functions for controlling gas animation. This new system uses aninverse particle system, where each point in three-dimensional screen space (image space discretized to pixel locations) is moved through a gas space to determine which portion of the gas occupies the current location in screen space.

External watchman routes

Abstract: We consider the problem of finding a shortest watchman route from which the exterior of a polygon is visible (external watchman route). We present an O (n4 log logn) algorithm to find shortest external watchman routes for simple polygons by transforming the external watchman route problem to a set of internal watchman route problems. Also, we present faster external watchman route algorithms for special cases. These include optimal O (n) algorithms for convex, monotone, star and spiral polygons and an O (n log logn) algorithm for rectilinear polygons.

Ray tracing general parametric surfaces using interval arithmetic

Abstract: This paper describes an algorithm for ray tracing general parametric surfaces. After dividing the surface adaptively into small parts, a binary tree of these parts is built. For each part a bounding volume is calculated with interval arithmetic. From linear approximations and intervals for the partial derivatives it is possible to construct parallelepipds that adapt the orientation and shape of the surface parts very well and form very tight enclosures. Therefore we can develop an algorithm for rendering that is similar to that used with Bezier and B-spline surfaces, where the bounding volumes are derived from the convex hull property. The tree of enclosures (generated once in a preprocessing step) guarantees that each ray that hits the surface leads to an iteration on a very small surface part; this iteration can be robustly (and very quickly) performed in real arithmetic.

Spherical splines and orientation interpolation

Abstract: This paper presents a method for designing spherical curves by two weighted spatial rotations. This approach is for the design of interpolating spherical curves and orientation interpolation. The same approach can be used for smoothing orientations or corners on a sphere. The designed curves have the following features: C1 continuity, local control, and invariance under orthogonal transformations of coordinate systems.

2D line and polygon clipping based on space subdivision

Abstract: This paper introduces a new approach to 2D line and polygon clipping against a rectangular clipping region, using space subdivision into cells, with the clipping region as the central cell. The line segment path is traced through the cells, and entries into and out of the cell corresponding to the clipping region enable computation of the intersection of the line segment with crossed cell edges. Tracing the line segment path is computationally very simple, leading to an algorithm that only computes intersections that the are part of the clipped line segment. The new algorithm is compared to other standard line clipping algorithms with simulations and operation counts.

3D-line clipping algorithms: a comparative study

Abstract: Some well-known line-polyhedron intersection methods are summed up and new accelerating modifications presented. Results of comparison of known and newly developed methods are included. New methods use the fact that each line can be described as the intersection of two planes.

Algorithms for computing the center of area of a convex polygon

Abstract: The center of area of a convex polygonP is the unique pointp * that maximizes the minimum area overlap betweenP and any halfplane that includesp *. We show thatp * is unique and present two algorithms for its computation. The first is a combinatorial algorithm that runs in timeO (n 6 log2 n). The second is a “numerical” algorithm that runs in timeO(GK(n+K)) whereK represents the number of desired bits of precision in the output coordinates andG the number of bits used to represent the coordinates of the input polygon vertices. We conclude with a discussion of implementation issues and related results.

An algorithm for recognizing palm polygons

Abstract: A polygonP is said to be apalm polygon if there exists a pointx∈P such that the Euclidean shortest path fromx to any pointy∈P makes only left turns or only right turns. The set of all such pointsx is called thepalm kernel. In this paper we propose an O(E) time algorithm for recognizing a palm polygonP, whereE is the size of the visibility graph ofP. The algorithm recognizes the given polygonP as a palm polygon by computing the palm kernel ofP. If the palm kernel is not empty,P is a palm polygon.

Multimouth surfaces for synthetic actor animation

Abstract: Most parts of the human body are cylindrical in shape. Generalized cylinders, with two cross-sectional openings, are a logical choice to represent these cylindrical shapes. However, a variety of human body regions can be visualized as surfaces with multiple openings or multimouth (MM) surfaces. Some examples of such surfaces are the pelvis, the chest, and the palms of the hands. We investigated the suitability of non-uniform rational B-spline (NURBS) formulation for creating multimouth surfaces. Two techniques, the surface wrapping model and the garland model, are presented.

The Superman problem

Abstract: Given a polygonK contained in a polygonP, and a points lying outsideP, we present a Θ (n logn) algorithm that finds the minimum number of edges, ofP that we want to retain in order to hidek froms Furthermore, if the visibility polygon ofs givenK is unbounded, the algorithm is shown to run in linear time This paper is dedicated to J Siegel and J Shuster

Clamping a polygon

Abstract: Aclamping hand has two opposing parallel edges; the distance between them can vary. We define what it means for the edges of a clamping hand and some edges of a polygon to form aclamp on the polygon. We conjecture that any polygon can be clamped by a hand if its edges are of positive length, but only provide proofs that clamps must exist for convex polygons and for certain polygons composed of two convex chains. The proofs involve extensive case analyses, and it is not obvious how to generalize them.

Generating a smooth voxel-based model from an irregular polygon mesh

Abstract: A method for generating a smooth voxelbased model from an arbitrary polygon mesh is presented. It is based on a polygonal subdivision process which takes an irregular polygon mesh as input and creates a finer and smoother mesh. The mesh is recursively refined down to or close to the voxel level, and then voxelized (digitized) into a voxel-based representation. A local subdivision approach has been developed in order to ease the computationally expensive subdivision process. The voxelization of the mesh maintains topological and fidelity requirements which are pre-defined and application dependent.

MARS: a tool-based modeling, animation, and parallel rendering system

Abstract: This paper describes a system for modeling, animating, previewing and rendering articulated objects. The system has a modeler of objects that consists of joints and segments. The animator interactively positions the articulated object in its stick, control vertex, or rectangular prism representation and previews the motion in real time. Then the data representing the motion and the models is sent to a multicomputer [iPSC/2 Hypercube (Intel)]. The frames are rendered in parallel, exploiting the coherence between successive frames, thus cutting down the rendering time significantly. Our main aim is to make a detailed study on rendering of a sequence of 3D scenes. The results show that due to an inherent correlation between the 3D scenes, an efficient rendering can be achieved.

An efficient algorithm for identifying objects using robot probes

Abstract: When robot finger probes are used to recognize objects,m-1 probes are necessary and sufficient to identify an object with a fixed orientation and position among a set ofm convex planarn-sided objects. An algorithm is presented to preprocess a set of objects for efficient probing, together with a probing scheme and algorithms to delete objects from or to insert objects into the set.

Visualizing Newton's Method on Fractional Exponents

Abstract: Newton's method for finding complex solutions of the equationzα−1=0 is investigated for real values of α. The bifurcations that occur, as the power α varies are illuminated with computer graphics. In particular, the appearance of an attracting 2-cycle just below even powers is investigated.

Anomalous color spaces and their structure

Abstract: A united color-perspective theory of Mobilevision (MV), a recently developed computer graphics technique, is described. The generalized (dynamic) perspective laws of MV are constructed with an algebraic structure of anomalous color spaces (the color spaces enlarged by overcolors, the interactively controlled color modulations). Such a structure is described by projective special unitary matrix — 3×3 [SU(3)]-hypermultiplets, 2D-quantum-field analogs of representations of the group SU (3) of symmetries of the ordinary 3D color space. A connection of the MV color technique with classical prototypes is described in such a way that its advantages with respect to modern techniques of computer graphics are high-lighted. The results of testing MV palettes and their use is given.

Digital halftoning by iterative isotropic error feedback

Abstract: An error diffusion scheme for digital halftoning is proposed. The scheme is an iterative and isotropic error feedback process. Also, to compensate for the nonlinear tone reproduction by laser printers due to ink drop overlaps, we incorporate Pappas-Neuhoff's simplified printer model into the new error diffusion scheme. It appears that the proposed halftoning technique enhances the perceived tone continuity of halftone hard copies, and it alleviates the objectionable structured halftone textures of some existing methods. In addition, a mechanism is suggested to preview a halftone print on a gray-level CRT monitor. The user can interactively set the desired brightness of the halftone print and balance image contrast and tone continuity, which are two mutually exclusive subjective criteria for halftone reproduction.

Shadows on bump-mapped surfaces in ray tracing

Abstract: This paper presents a method of generating shadows on bump-mapped surfaces in ray tracing. The method yields images with realistic shadows influenced by bumpy surface geometry. In our method, intersections are calculated between eye/reflection/refraction rays and ‘smooth’ original surfaces as usual, and the surfaces and shaded according to Blinn's bump mapping. For shadowing, however, we shift the intersection points based on the approximated bumpy surface shape, and the shadow rays are fired from the shifted intersection points. Since the method involves no explicit intersection calculation between rays and bumpy surfaces, it requires only a small amount of computation in addition to conventional ray tracting. It is easy to insert the method into existing ray tracers, and it can be applied to variants of ray tracing algorithms that use shadow rays.

3D representation of the Mandelbrot set

Abstract: A new 3D representation of the Mandelbrot set is presented. Although the method employing the Douady Hubbard's potential function has been useful for the 3D representation of the Mandelbrot set, in our new method 3D pictures are generated by setting height components normal to the plane of the original Mandelbrot set. The pictures obtained look like natural landscapes with cliffs.