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29
Modeling the Mighty Maple
"... A method is presented for representing botanical trees, given threedimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A freeform surface connects branching limbs. "Blobby" techniques are used to model th ..."
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Cited by 108 (1 self)
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A method is presented for representing botanical trees, given threedimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A freeform surface connects branching limbs. "Blobby" techniques are used to model the tree trunk as a series of noncircular cross sections. Bark is simulated with a bump map digitized from real world bark; leaves are textures mapped onto simple surfaces.
Polar Forms for Geometrically Continuous Spline Curves of Arbitrary Degree
 ACM Trans. Graph
, 1993
"... This paper studies geometrically continuous spline curves of arbitrary degree. Based on the concept of universal splines we obtain geometric constructions for both the spline control points and for the B'ezier points and give algorithms for computing locally supported basis functions and for kn ..."
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Cited by 18 (2 self)
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This paper studies geometrically continuous spline curves of arbitrary degree. Based on the concept of universal splines we obtain geometric constructions for both the spline control points and for the B'ezier points and give algorithms for computing locally supported basis functions and for knot insertion. The geometric constructions are based on the intersection of osculating flats. The concept of universal splines is defined in such a way that these intersections are guaranteed to exist. As a result of this development we obtain a generalization of polar forms to geometrically continuous spline curves by intersecting osculating flats. The presented algorithms have been coded in Maple, and concrete examples illustrate the approach. Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling  curve, surface, solid, and object representations General Terms: Algorithms, Design Additional Key Words and Phrases: B'ezier point, blossom, de...
Geometric continuity, shape parameters, and geometric constructions for catmullrom splines
 ACM Trans. Graph
, 1988
"... CatmullRom splines have local control, can be either approximating or interpolating, and are efficiently computable. Experience with Betasplines has shown that it is useful to endow a spline with shape parameters, used to modify the shape of the curve or surface independently of the defining contr ..."
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Cited by 14 (1 self)
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CatmullRom splines have local control, can be either approximating or interpolating, and are efficiently computable. Experience with Betasplines has shown that it is useful to endow a spline with shape parameters, used to modify the shape of the curve or surface independently of the defining control vertices. Thus it is desirable to construct a subclass of the CatmullRom splines that has shape parameters. We present such a class, some members of which are interpolating and others approximating. As was done for the Betaspline, shape parameters are introduced by requiring geometric rather than parametric continuity. Splines in this class are defined by a set of control vertices and a set of shape parameter values. The shape parameters may be applied globally, affecting the entire curve, or they may be modified locally, affecting only a portion of the curve near the corresponding joint. We show that this class results from combining geometrically continuous (Betaspline) blending functions with a new set of geometrically continuous interpolating functions related to the classical Lagrange curves. We demonstrate the practicality of several members of the class by developing efficient computational algorithms. These algorithms are based on geometric constructions that take as input a control polygon and a set of shape parameter values and produce as output a sequence of Bizier control
Smooth parametric surfaces and Nsided patches
 Computation of Curves and Surfaces
, 1990
"... CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an nsided hole occurring within a smooth rectangular patch complex. A number of solutions to this proble ..."
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Cited by 11 (0 self)
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CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an nsided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed. 1.
Computer graphics for water modeling and rendering: a survey
 Future Generation Computer Systems
, 2004
"... A key topic in computer graphics is the realistic representation of natural phenomena. Among the natural objects, one of the most interesting (and most difficult to deal with) is water. Its inherent complexity, far beyond that of most artificial objects, represents an irresistible challenge for the ..."
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Cited by 9 (0 self)
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A key topic in computer graphics is the realistic representation of natural phenomena. Among the natural objects, one of the most interesting (and most difficult to deal with) is water. Its inherent complexity, far beyond that of most artificial objects, represents an irresistible challenge for the computer graphics world. Thus, during the last two decades we have witnessed an increasing number of papers addressing this problem from several points of view. However, the computer graphics community still lacks a survey classifying the vast literature on this topic, which is certainly unorganized and dispersed and hence, difficult to follow. This paper aims to fill this gap by offering a historical survey on the most relevant computer graphics techniques developed during the 1980s and 1990s for realistic modeling, rendering and animation of water.
Grafield: Fielddirected dynamic splines for interactive motion control
 In Eurographics'88
, 1988
"... AbstractThis paper presents an interactive system for motion control that emphasizes object interaction. The fundamental mechanism provided to support interaction between objects is thefield. We present a new technique called dynamic splines which dynamically generates a trajectory under field con ..."
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Cited by 9 (1 self)
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AbstractThis paper presents an interactive system for motion control that emphasizes object interaction. The fundamental mechanism provided to support interaction between objects is thefield. We present a new technique called dynamic splines which dynamically generates a trajectory under field control. Dynamic splines mimic the kinematic behaviour of a particle moving in a field, yet, it is computationally inexpensive compared to full physical dynamic approaches. We also show how to extend the field approach to specify tracking behaviour. 1.
Scalar Tagged PN Triangles
, 2005
"... This paper presents a new technique to convert a coarse polygonal geometric model into a smooth surface interpolating the mesh vertices, by improving the principle proposed by Vlachos et al. in their "Curved PNTriangles". ..."
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Cited by 9 (3 self)
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This paper presents a new technique to convert a coarse polygonal geometric model into a smooth surface interpolating the mesh vertices, by improving the principle proposed by Vlachos et al. in their "Curved PNTriangles".
Detecting Cusps and Inflection Points in Curves
 Comp. Aided Geom. Design
, 1992
"... In many applications it is desirable to analyze parametric curves for undesirable features like cusps and inflection points. Previously known algorithms to analyze such features are limited to cubics and in many cases are for planar curves only. We present a general purpose method to detect cusps in ..."
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Cited by 8 (1 self)
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In many applications it is desirable to analyze parametric curves for undesirable features like cusps and inflection points. Previously known algorithms to analyze such features are limited to cubics and in many cases are for planar curves only. We present a general purpose method to detect cusps in polynomial or rational space curves of arbitrary degree. If a curve has no cusp in its defining interval, it has a regular parametrization and our algorithm computes that. In particular, we show that if a curve has a proper parametrization then the necessary and sufficient condition for the existence of cusps is given by the vanishing of the first derivative vector. We present a simple algorithm to compute the proper parametrization of a polynomial curve and reduce the problem of detecting cusps in a rational curve to that of a polynomial curve. Finally, we use the regular parametrizations to analyze for inflection points.
Intrinsic stabilizers of planar curves
 IN THIRD EUROPEAN CONFERENCE ON COMPUTER VISION (ECCV'94
, 1994
"... Regularization offers a powerful framework for signal reconstruction by enforcing weak constraints through the use of stabilizers. Stabilizers are functionals measuring the degree of smoothness of a surface. The nature of those functionals constrains the properties of the reconstructed signal. In th ..."
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Cited by 7 (5 self)
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Regularization offers a powerful framework for signal reconstruction by enforcing weak constraints through the use of stabilizers. Stabilizers are functionals measuring the degree of smoothness of a surface. The nature of those functionals constrains the properties of the reconstructed signal. In this paper, we first analyze the invariance of stabilizers with respect to size, transformation and their ability to control scale at which the smoothness is evaluated. Tikhonov stabilizers are widely used in computer vision, even though they do not incorporate any notion of scale and may result in serious shape distortion. We first introduce an extension of Tikhonov stabilizers that offers natural scale control of regularity. We then introduce the intrinsic stabilizers for planar curves that apply smoothness constraints on the curvature pro le instead of the parameter space.