EP0504889A2
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Methods for generating free curves and sculptured surfaces
Assignee: Sony Corp
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Filing: 1992-03-19
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Granted: —
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Expires: 2012-03-19
Abstract
Abstract Disclosed are methods for generating free curves and sculptured surfaces illustratively for use with a CAD/CAM designing apparatus whereby Bezier curves and surfaces are readily generated with reference to point sequences, point groups and surfaces. In operation, a starting point (P0) and an end point (P3) for a sequence of points (q1, q2...) are set as nodes, and a free curve (R(t)) is temporarily established thereby. Then control points are repeatedly established to minimize the shortest distances between the points (q1, q2...) in the sequence and the free curve (R(t)). By use of the coordinates of a plurality of points, the shortest distance (d1, d2...) is found between each of these points (q1, q2...) and a reference patch. The internal control points are set so as to minimize the total sum of these shortest distances. When a patch is generated whose external shape is represented by a plurality of points, with another plurality of points also set on the reference patch for modification, a Bezier surface is generated with respect to these point groups and surfaces.
Inventors
- 👤 Miwa Ooka
- 👤 Tetsuzo Kuragano
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-11-09 00:12
CPC Classifications
G; G06; G06F; G06F17/00; G06T; G06T17/00; G06T17/20
Claims Analysis
Total Claims: 8
Claim 1
Independent Claim
196 words
A method for generating a free curve expressed by a vector function using a predetermined parameter on the basis of two nodes having control points interposed therebetween in a cubic space, said method comprising the steps of: establishing to said two nodes a starting point (P0) and an end point (P3) of an input point sequence (q1, q2,...qm); temporarily establishing said control points based on points in said point sequence, said points in said point sequence being adjacent to said starting point and to said end point; drawing perpendiculars (d2, d3...) from the points constituting said point sequence to said free curve (R(t)) vector determined by said nodes and by said control points, said perpendiculars being drawn so as to find parameters of the intersection points formed between said perpendiculars and said free curve (R(t)); reestablishing said control points so as to minimize the total sum of distances between the points in said point sequence on the one hand, and said intersection points defined by said parameters on said free curve (R(t)) on the other; and generating said free curve approximating said point sequence by use of the established nodes and of the reestablished control points.
Claim 2
Dependent Claim
47 words
A method for generating a free curve according to claim 1, wherein said total sum of said distances to said free curve (R(t)) is a square-sum, said square-sum being inserted into simultaneous linear equations with two unknowns, said simultaneous linear equations being solved to find control points.
Claim 3
Independent Claim
105 words
A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function on the basis of internal control points (P00...) established in said frame space enclosed by boundary curves (COM1...) in a cubic space, said method comprising the steps of: detecting the shortest distances (di), based on the coordinate data of a plurality of points (q1, q2,...), between said plurality of points on the one hand and said patch serving as reference on the other; and generating said patch by establishing said internal control points so as to minimize the total sum of said shortest distances.
Claim 4
Dependent Claim
46 words
A method for generating a sculptured surface according to claim 3, wherein said total sum of said distances to said sculptured surface is a square-sum, said square-sum being inserted into simultaneous linear equations with two unknowns, said simultaneous linear equations being solved to find control points.
Claim 5
Independent Claim
117 words
A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function on the basis of internal control points (P00...) established in said frame space enclosed by boundary curves (COM1...) in a cubic space, said method comprising the steps of: detecting the shortest distances between a plurality of points on the one hand, and said patch formed in said frame space on the other; establishing said internal control points (P00...) in said frame space containing said patch so as to minimize the total sum of said shortest distances; and generating a patch in such a manner that the external shape thereof is expressed by said plurality of points.
Claim 6
Independent Claim
152 words
A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function on the basis of internal control points (P00...) established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: establishing a plurality of points (q1, q2,...) on a patch to be modified; detecting the shortest distances (d1, d2,...) between said plurality of points on the one hand, and a reference patch for modification on the other; establishing said internal control points (P00...) within said frame space of said patch to be modified, the establishing of said internal control points being performed in such a manner as to minimize the total sum of said shortest distances; and generating a patch approximating the surface shape of said reference patch for modification, said patch being generated within said frame space of said patch to be modified.
Claim 7
Independent Claim
32 words
A method for generating a sculptured surface according to one of claims 3 through 6, wherein said sculptured surface as it is being generated is made visible on a display unit (16).
Claim 8
Independent Claim
32 words
A method for generating a sculptured surface according to one of claims 3 through 7, wherein said sculptured surface after it has been generated (13) represents data for preparing a tool path.
References Cited (Backward Citations)
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