Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Computer Aided Geometric Design
Simplicial pivoting for mesh generation of implicitly defined surfaces
Computer Aided Geometric Design
Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
Topologically reliable display of algebraic curves
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Counting real zeros
A hybrid symbolic-numerical method for tracing surface-to-surface intersections
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Bridging the gap between CSG and Brep via a triple ray representation
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Implicit linear interval estimations
SCCG '02 Proceedings of the 18th spring conference on Computer graphics
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Novel techniques for robust voxelization and visualization of implicit surfaces
Graphical Models - Volume modeling
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Point rendering of non-manifold surfaces with features
Proceedings of the 5th international conference on Computer graphics and interactive techniques in Australia and Southeast Asia
Querying continuous functions in a database system
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
A local fitting algorithm for converting planar curves to B-splines
Computer Aided Geometric Design
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Fast continuous collision detection using deforming non-penetration filters
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Arbitrary 3d resolution discrete ray tracing of implicit surfaces
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Empirical study of an evaluation-based subdivision algorithm for complex root isolation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
Hardware architecture for voxelization-based volume rendering unstructured grids
EGGH'95 Proceedings of the Tenth Eurographics conference on Graphics Hardware
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A new, recursive, space-subdivision algorithm for rasterizing algebraic curves and surfaces gets its accuracy from a newly devised, computationally efficient, and asymptotically correct test. The approach followed is essentially the interval arithmetic method for rendering implicit curves. The author's contribution is a particularly efficient way to construct inclusion functions for polynomials. An ideal algorithm is given for rendering an algebraic curve Z(f)={(x,y):f(x,y)=0} in a square box of side n. The algorithm scans the square and paints only those pixels cut by the curve. This algorithm is ideal, because every correct algorithm should paint exactly the same pixels, but it is impractical. It requires n/sup 2/ test evaluations, one for each pixel in the square. However, since in general it will be rendering a curve on a planar region, the number of pixels it is expected to paint is only O(n). We need a more efficient algorithm. There are two issues to examine. The first is how to reduce the computational complexity by recursive subdivision. The second is how to test whether the curve Z(f) cuts a square.