The Scale Method for Blending Operations in Functionally‐Based Constructive Geometry

Hsu, Pi-Chung; Lee, C.

doi:10.1111/1467-8659.00656

Cited by 18 publications

(28 citation statements)

References 22 publications

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“…Recently Barthe et al 30 and Hsu et al 17 introduced new CSG opertors with smooth transitions. In Hsu et al, operators can be n-ary and a lot of flexibility is provided in the choice of the function defining the operator.…”

Section: /mentioning

confidence: 99%

“…Unbounded representation provides a general implicit volume representation 13 and therefore, a wide variety of modelling operators such as sweeping by moving solids 14 , Boolean composition with soft transition 9 > 15 > 16 > 17 and Constructive Volume Geometry algebra 18 , have been proposed. Due to their global definition, it is difficult to provide both accurate and interactive surface rendering 30 .…”

Section: Introductionmentioning

confidence: 99%

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Controllable Binary CSG Operators for "Soft Objects"

Barthe¹,

Wyvill²,

Groot³

2004

Int. J. Shape Model.

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Potential functions allow the definition of both an implicit surface and its volume. In this representation, two categories can be distinguished: bounded and unbounded representations. Boolean composition operators are standard modelling tools allowing complex objects to be built by the combination of simple volume primitives. Though they are well denned for the second category, there is no clear definition of the properties that such operators should satisfy in order to provide bounded representation with both smooth and sharp transition. In this paper, we focus on bounded implicit representation. We first present fundamental properties to create adequate composition operators. From this theoretical framework, we derive a set of Boolean operators providing union, intersection and difference with or without smooth transition. Our new operators integrate accurate point-by-point control of smooth transitions and they generate G 1 continuous potential fields even when sharp transition operators are used.

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Section: /mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controllable Binary CSG Operators for "Soft Objects"

Barthe¹,

Wyvill²,

Groot³

2004

Int. J. Shape Model.

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“…Furthermore, the blends in 19 , 20 offered blending range parametersto adjust the blending region for soft object modeling.For example, the scale method 20 gave a scale union B SA ( x 1 , x 2 ) with a curvature parameter p and blending rangeparameters r 1 and r 2 . Adjusting r 1 and r 2 can limit theblending surface B SA ( f 1 , f 2 ) = 0.5 in the blending region { X ∈ R 3 | 0.5(1 − r 1 ) ≤ f 1 ( X ) ≤ 0.5 and 0.5(1 − r 2 ) ≤ f 2 ( X ) ≤ 0.5},and f 1 = 0.5 and f 2 = 0.5 are deformed locally.…”

Section: Previous Workmentioning

confidence: 99%

“…As a result, the sizes of theseblending surfaces above depend completely on the sizes ofblended primitives. Even though blending operators in 19 , 20 can change the blending region by adjusting the blendingrange parameters, they are computationally more expensiveand their blending surfaces still can not exceed the sizes ofblended primitives.…”

Section: Introductionmentioning

confidence: 99%

Field Functions for Blending Range Controls on Soft Objects

Hsu

Lee

2003

Computer Graphics Forum

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This paper proposes new field functions that have adjustable inner radius and outer radius of influence. Incorporatingthe proposed field functions with soft object modeling, soft blending, Ricci's super‐ellipsoid blends, Perlin'sset operations, and R‐functions, etc. can have blending range controls by adjusting the inner and the outer radiiof influence of given field functions. As a result, the sizes of the resulting blending surfaces on soft objects willnot be restricted by the sizes of the blended primitive soft objects and can be enlarged and shrunk freely withoutdeforming the overall shapes of blended primitive soft objects. In addition, a small soft object can have a largeblending region, and a large one can have a small blending region Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling ‐ Curve, surface, solid and object representations

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“…In the literature, many defining functions were developed, including generalized distance functions [5], super-quadrics [6], generalized distance metrics [7], super-ellipsoids [8]- [10], cylinders [11], sweep objects [12] and hyper-quadrics [13]. Among these functions above, super-quadrics [2] can be represented parametrically, too, and briefly they have both the advantages of implicit and parametric surfaces.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric and Symmetric Spherical Product Surfaces with both Implicit and Parametric Representations

Hsu¹

2013

IJMO

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Abstract-This paper proposes spherical product functions to define implicit spherical product surfaces. A spherical product function is composed of a contour function and a profile function and its iso-surface's shape is generated by modulating and translating the iso-curve of the contour function through the points on the iso-curve of the profile function. This paper also shows if contour and profile functions are ray-linear, then an implicit spherical product surface can be parameterized and hence have both the advantages of implicit and parametric surfaces. Moreover, this paper proposes ray-linear two-branch and one-branch linear and super-hyperbolic functions that can be used to construct new contour and profile functions with asymmetric or symmetric iso-curves. Based on them, an implicit spherical product surface can has asymmetric or symmetric contour and profile and also has a parametric representation.Index Terms-Implicit surface, blending operations, parametric surface.

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The Scale Method for Blending Operations in Functionally‐Based Constructive Geometry

Cited by 18 publications

References 22 publications

Controllable Binary CSG Operators for "Soft Objects"

Controllable Binary CSG Operators for "Soft Objects"

Field Functions for Blending Range Controls on Soft Objects

Asymmetric and Symmetric Spherical Product Surfaces with both Implicit and Parametric Representations

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