Rational blending surfaces between quadrics

Johannes Wallner; Helmut Pottmann

doi:10.1016/S0167-8396(96)00037-4

Rational blending surfaces between quadrics

Johannes Wallner, Helmut Pottmann^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C¹ blends between these surfaces, such that interactive design of trim lines and surface tension is possible. The lowest possible degree of a blend that can be achieved with this method is (4, 3).

Original language	English (US)
Pages (from-to)	407-419
Number of pages	13
Journal	Computer Aided Geometric Design
Volume	14
Issue number	5
DOIs	https://doi.org/10.1016/S0167-8396(96)00037-4
State	Published - Jun 1997
Externally published	Yes

Keywords

Blending surface
Kinematic mapping
Line geometry
NURBS surface

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/S0167-8396(96)00037-4

Cite this

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title = "Rational blending surfaces between quadrics",

abstract = "Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C1 blends between these surfaces, such that interactive design of trim lines and surface tension is possible. The lowest possible degree of a blend that can be achieved with this method is (4, 3).",

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author = "Johannes Wallner and Helmut Pottmann",

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AU - Wallner, Johannes

AU - Pottmann, Helmut

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N2 - Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C1 blends between these surfaces, such that interactive design of trim lines and surface tension is possible. The lowest possible degree of a blend that can be achieved with this method is (4, 3).

AB - Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C1 blends between these surfaces, such that interactive design of trim lines and surface tension is possible. The lowest possible degree of a blend that can be achieved with this method is (4, 3).

KW - Blending surface

KW - Kinematic mapping

KW - Line geometry

KW - NURBS surface

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U2 - 10.1016/S0167-8396(96)00037-4

DO - 10.1016/S0167-8396(96)00037-4

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VL - 14

SP - 407

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JO - Computer Aided Geometric Design

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ER -

Rational blending surfaces between quadrics

Abstract

Keywords

ASJC Scopus subject areas

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