Patent
1991-10-08
1996-01-02
Herndon, Heather R.
G06T 1720
Patent
active
054816599
DESCRIPTION:
BRIEF SUMMARY
TECHNICAL FIELD
The present invention is directed generally to a method for generating free-form surface data, and more particularly, to a method suited to generate the free-form surface data employed for CAD (Computer Aided Design) or CAM (Computer Aided Manufacturing).
BACKGROUND ARTS
In the case of designing a geometry (geometric modeling) of an object assuming free-form surfaces by, e.g., a CAD-based method, a designer typically has hitherto created a surface expressed by a so-called wire frame. The creation thereof involves the steps of specifying a plurality of points (referred to as nodes) in a three-dimensional space through which the surface passes and causing a computer to compute a boundary curvilinear network which connects the plurality of specified nodes by use of predetermined functions.
It is thus possible to form a multiplicity of frame spaces encircled by the boundary curves (this type of process is hereinafter referred to as frame processing).
The boundary curvilinear network itself, which is formed by this frame processing, represents a rough geometry of the object that the designer intends to design. If a surface expressible by a predetermined vector function can be obtained by an interpolative computation in combination with the boundary curves encircling the respective frame spaces, it is feasible to create a free-form surface (which can not be prescribed by quadric functions) designed by the designer on the whole.
The surface stretched over the individual frame space constitutes a fundamental element which in turn forms the whole surface. This is known as a patch.
In this type of conventional CAD system, a cubic tensor product based on, e.g., easy-to-calculate Bezier formula and B-spline formula is employed as a vector function representing the boundary curvilinear network. The cubic tensor product is considered to be optimal to a mathematical expression of the free-form surface exhibiting no special characteristic in terms of geometry.
More specifically, in the free-form surface with no special geometric characteristic, when projecting points given in the space on an X-Y plane, the points projected thereon are in the great majority of cases arranged in regular matrices. It is a known fact that when the number of these projected points is expressed by m x n, the frame space concerned can easily be stretched by use of a quadrilateral patch expressed by the cubic Bezier formula.
This mathematical expression, however, involves a difficulty in the way of connecting the patches to each other, if applied to a surface exhibiting a geometric characteristic (for instance, a surface assuming a largely skewed geometry). It is required that a high-level mathematical computation be executed, and hence there arises a problem to make computer-based arithmetic operations complicated and huge.
Especially when framing the surface assuming an extremely skewed geometry, most of arrays of the specified points do not have any regularity. Therefore, the method of stretching the quadrilateral patch in the frame space is actually attended with a difficulty to shape a smooth free-form surface.
Proposed under such circumstances was a free-form surface preparing method (Japanese Patent application No. 15396/1986) arranged such that the frame space is shaped by using not the conventional quadrilateral patch but a so-called trilateral patch in which three ways are closed by, e.g., cubic Bezier curves.
Based on this free-form surface generating method, a boundary curve representing a boundary of the frame space undergoing frame processing and patch vectors T stretched over the frame spaces are namely given by the following formulae: ##EQU1## (Where, vector P.sub.x =vector P.sub.(11))
As shown above, there is adopted an expression which uses the vector function vector T based on the cubic Bezier formula.
Note that w in the formula (1) is expressed by the following formula: by use of a vector function vector T.sub.(u,v) as shown in the following formula:
As a matter of fact, a vector P.sub.(00) in the formulae
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Patent Abstracts of Japan, vol. 012, No. 429 (P-785), 14 Nov. 1988 & JP-A-63 159 981 (Sony Corp.), 2 Jul. 1988.
Patent Abstracts of Japan, vol. 012, No. 429 (P-785), 14 Nov. 1988 & JP-A-63 159 982 (Sony Corp.), 2 Jul. 1988.
Proceedings IECON, '86 Sep. 1986, Milwaukee, USA, pp. 61-66; N. Nakajima et al.: "Direct Generation of Solid Model from Wire-Frame Model in CAD System".
Kuragano Tetsuzo
Nosaka Shiro
Fetting Anton W.
Herndon Heather R.
Sony Corporation
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