System for blending surfaces in geometric modeling

• US 5,251,160 A
• Filed: 08/27/1991
• Issued: 10/05/1993
• Est. Priority Date: 02/23/1988
• Status: Expired due to Fees

• Current Assignee: PTC Inc.
• Original Assignee: Evans & Sutherland Computer Corp. (Elevate Entertainment, Inc.)
• Inventors: Rockwood, Alyn P., Owen, John C.
• Primary Examiner(s): Black, Thomas G.
• Assistant Examiner(s): ZANELLI, MICHAEL J
• Application Number:
  US07/750,690
• Time in Patent Office: 770 Days
• Field of Search: 364/512, 364/514, 358/133, 358/163, 340/728, 340/729, 340/730, 382/54, 382/55, 395/155, 395/141, 395/118, 395/120, 395/119, 395/142, 395/143
• US Class Current: 703/2
• CPC Class Codes: G06T 17/00 Three dimensional [3D] modelling, e.g. data description of 3D objects

Abstract

A computer-aided design system and a process generates a graphic display of a blend between a plurality of geometric primitive shapes including other blends. An interactive terminal controls a geometric modeler to generate and modify visual graphic displays of primitive geometric shapes at a display screen of the interactive terminal. Logic structures generate both a blend and blends. Each logic structure is implemented with an individual distinct blending algorithm to accomplish a localized superelliptical blend and blends according to user selections including: a plurality of geometric primitive shapes to be blended, a blend operation, and a blend function. A memory, registers and gates in the system store and manage data.

Claims

1. A computer-aided design system for use with an interactive terminal for generating a graphic display of a localized superelliptical blend and blends between a plurality of geometric primitive shapes, said geometric primitive shapes including bland and blends which are truncated such that only a part of said blend and blends between predetermined locations of said geometric primitive shapes is generated said system comprising:

central processing means to generate and modify said graphic display of said geometric primitive shapes at said interactive terminal; and

blend processing means which comprises;

a logic structure for implementing geometric blending operations and geometric blending functions on said pixels for truncating said blend and blends to generate said localized superelliptical blend and blends for said graphic display, wherein said logic structure generates said blend and blends in accordance with an expression;

space="preserve" listing-type="equation">N<

P.sub.i >

=R<

P.sub.i >

{1-(Σ

.sub.i Q.sub.i).sup.1/5 }

where

space="preserve" listing-type="equation">R<

P.sub.i >

=Σ

.sub.i (Q.sub.i /Σ

.sub.i Q.sub.i)R.sub.i

and

space="preserve" listing-type="equation">Q.sub.i =[1-P.sub.i /R.sub.i ].sup.t.sub.+

wherein N<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R<

P_i >

=rescaling function corresponding to a non-Euclidean distance measure of said blend and blends from a zero surface of a selected geometric primitive shape within said blend and blends,

R_i =variable range defining bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, a constant which determines a degree of curvature of said blend and blends,

register means, operatively connected to said central processing means, for temporary storage of said geometric primitive shapes and said generated blend and blends from said blend processing means.

2. The system according to claim 1 wherein said blending processing means further comprises another logic structure generating said blend and blends in accordance with another expression:

space="preserve" listing-type="equation">N<

P.sub.i >

=R<

P.sub.i >

{Σ

.sub.i Q.sub.i).sup.(1/t) -1}

where

space="preserve" listing-type="equation">R<

P.sub.i >

=Σ

.sub.i (Q.sub.i /Σ

.sub.i Q.sub.i)R.sub.i

and

space="preserve" listing-type="equation">Z.sub.i =[1+P.sub.i /R.sub.i ].sup.t.sub.+

wherein

N<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R<

P_i >

=rescaling function corresponding to said non-Euclidean distance measure of said blend and blends from said zero surface of said selected geometric primitive shape within said blend and blends,

R_i =variable range defining said bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, said constant which determines said degree of curvature of said blend and blends.

9. The system according to claim 1 or 3 further including a discontinuity detection means for detecting error conditions that may occur in generating said blend and blends.

10. The system according to claims 1 or 3 wherein said blending processing means further comprises a plurality of logic structures each implementing an individually distinct geometric blending logic for generating said localized superelliptical blend and blends.

11. The system according to claims 1, 3, 5 or 7 wherein said interactive terminal includes a display screen and a keyboard.

12. The system according to claims 1, 3, 5 or 7 wherein said central processing means is further in communication with a memory.

13. The system according to claims 1, 3, 5 or 7 wherein said register means are operatively connected to said central processing means by input and output busses.

3. A computer-aided design system for use with an interactive terminal for generating a graphic display of a localized superelliptical blend and blends between a plurality of geometric primitive shapes, said geometric primitive shapes including blend and blends, comprising:

central processing means to generate and modify pixels on said graphic display of said geometric primitive shapes at said interactive terminal; and

blend processing means which comprises;

a logic structure for implementing geometric blending operations and geometric blending functions on said pixels to generate said localized superelliptical blend and blends for said graphic display, wherein said logic structure generates said blend and blends in accordance with an expression;

space="preserve" listing-type="equation">N<

P.sub.i >

=R<

P.sub.i >

{Σ

.sub.i Q.sub.i).sup.(1/t) -1}

where

space="preserve" listing-type="equation">R<

P.sub.i >

=Σ

.sub.i (Q.sub.i /Σ

.sub.i Q.sub.i)R.sub.i

and

space="preserve" listing-type="equation">Q.sub.i =[1+P.sub.i /R.sub.i ].sup.t.sub.+

wherein N<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R<

P_i >

=rescaling function corresponding to a non-Euclidean distance measure of said blend and blends from a zero surface of a selected geometric primitive shape within said blend and blends,

R_i =variable range defining bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, a constant which determines a degree of curvature of said blend and blends,

register means, operatively connected to said central processing means, for temporary storage of said geometric primitive shapes and said generated blend and blends from said blend processing means.

4. The system according to claim 3 wherein said blending processing means further comprises another logic structure generating said blend and blends in accordance with another expression:

space="preserve" listing-type="equation">N<

P.sub.i >

=R<

P.sub.i >

{1-(Σ

.sub.i Q.sub.i).sup.1/t }

where

space="preserve" listing-type="equation">R<

P.sub.i >

=Σ

.sub.i (Q.sub.i /Σ

.sub.i Q.sub.i)R.sub.i

and

space="preserve" listing-type="equation">Q.sub.i =[1-P.sub.i /R.sub.i ].sup.t.sub.+

wherein N<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R<

P_i >

=rescaling function corresponding to said non-Euclidean distance measure of said blend and blends from said zero surface of said selected geometric primitive shape within said blend and blends,

R_i =variable range defining said bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, said constant which determines said degree of curvature of said blend and blends.

5. A computer-aided design system for use with an interactive terminal for generating a graphic display of a localized superelliptical blend and blends between a plurality of geometric primitive shapes, said geometric primitive shapes including blend and blends which are truncated such that only a part of said blend and blends between predetermined locations of said geometric primitive shapes is generated, said system comprising:

central processing means to generate and modify pixels on said graphic display of said geometric primitive shapes at said interactive terminal; and

blend processing means for generating said blend and blends, which blending processing means comprises;

a logic structure for implementing geometric blending operations and geometric blending functions on said pixels to generate said localized superelliptical blend and blends for said graphic display, said geometric blending operations and said geometric blending functions being determinative of blend and blends shapes, wherein said logic structure generates said blend and blends in accordance with an expression;

space="preserve" listing-type="equation">D<

P.sub.i >

=h

where h is the root of S<

P_i -h>

=0, thus as a quantity, h has a value reducing S<

P_i -h>

to zero,

and S<

P_i -h>

=1-Σ

_i [1-(P_i -h)/R_i ]^t₊ =0

wherein h is a displacement of said blend and blends from a selected geometric primitive shape P_i indexed by i,

D<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R_i =variable range defining bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, a constant which determines a degree of curvature of said blend and blends,

register means, operatively connected to said central processing means, for temporary storage of said geometric primitive shapes and said generated blend and blends from said blend processing means.

6. The system according to claim 5 wherein said blending processing means further comprises another logic structure generating said blend and blends in accordance with another expression:

space="preserve" listing-type="equation">D<

P.sub.i >

=h,

where h is the root of S<

P_i -h>

=0, thus as said quantity, h has said value reducing S<

P_i -h>

to zero,

and S<

P_i -h>

=Σ

_i [1+(P_i -h/R_i ]^t₊ -1=0

wherein h is said displacement of said blend and blends from said selected geometric primitive shape P_i,

D<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R_i =variable range defining said bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, said constant which determines said degree of curvature of said blend and blends.

7. A computer-aided design system for use with an interactive terminal for generating a graphic display of a localized superelliptical blend and blends between a plurality of geometric primitive shapes, said geometric primitive shapes including blend and blends which are truncated such that only a part of said blend and blends between predetermined locations of said geometric primitive shapes is generated, said system comprising:

central processing means to generate and modify pixels of said graphic display of said geometric primitive shapes at said interactive terminal; and

blend processing means for generating said blend and blends, which said blending processing means comprises;

a logic structure for implementing geometric blending operations and geometric blending functions on said pixels to generate said localized superelliptical blend and blends for said graphic display, said geometric blending operations and said geometric blending functions being determinative of blend and blends methods, wherein said logic structure generates said blend and blends in accordance with an expression;

space="preserve" listing-type="equation">D<

P.sub.i >

=h,

where h is the root of S<

P_i -h>

=0, thus as a quantity, h has a value reducing S<

P_i -h>

to zero,

and S<

P_i -h>

=Σ

_i [1+)P_i -h/R_i ]^t₊ -1=0

wherein h is a displacement of said blend and blends from a selected geometric primitive shape P_i indexed by i,

D<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R_i =variable range defining bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, a constant which determines a degree of curvature of said blend and blends,

register means, operatively connected to said central processing means, for temporary storage of said geometric primitive shapes and said generated blend and blends from said blend processing means.

8. The system according to claim 7 wherein said blending processing means further comprises another logic structure generating said blend and blends in accordance with another expression:

space="preserve" listing-type="equation">D<

P.sub.i >

=h

where h is the root of S<

P_i -h>

=0, thus as said quantity, h has said value reducing S<

P_i -h>

to zero,

and S<

P_i -h>

=1-Σ

_i [1-(P_i -h)/R_i]^t₊ =0

wherein h is said displacement of said blend and blends from said selected geometric primitive shape P_i indexed by i,

D<

P_i >

defines said localized superelliptical blend and blends between said geometric primitive shapes,

R_i =variable range defining said bounds of said blend and blends,

P_i =implicit function defining said selected geometric primitive shape indexed by i, and

t=thumbweight, said constant which determines said degree of curvature of said blend and blends.

14. A computer-aided design system for use with an interactive terminal for generating a graphic display of a localized superelliptical blend and blends between a plurality of geometric primitive shapes, including blend and blends, which blend and blends are truncated such that only a part of said blend and blends between predetermined locations of said plurality of geometric shapes is generated, said system comprising:

central processing means to generate and modify pixels on said graphic display of certain selected primitive geometric shapes of said plurality of geometric primitive shapes at said interactive terminal; and

blend processing means for generating blending surfaces from said certain selected geometric primitive shapes, which said blending processing means comprises;

logic structures for selectively altering mass of said certain selected geometric primitive shapes and for selectively determining distances between zero surfaces of said blending surfaces and said certain selected geometric primitive shapes to generate said localized superelliptical blend and blends for said pixels of said graphic display, one of said logic structures generating said localized superelliptical blend and blends in accordance with an expression;

space="preserve" listing-type="equation">N<

P.sub.i >

=R<

P.sub.i >

{1-(Σ

.sub.i Q.sub.i).sup.1/t }

where

space="preserve" listing-type="equation">R<

P.sub.i >

=Σ

.sub.i (Q.sub.i /Σ

.sub.i Q.sub.i)R.sub.i

and

space="preserve" listing-type="equation">Q.sub.i =[1-P.sub.i /R.sub.i ].sup.t.sub.+

wherein N<

P_i >

defines said localized superelliptical blend and blends between said certain selected geometric primitive shapes,

R<

P_i >

=rescaling function corresponding to a non-Euclidean distance measure of said blend and blends from said zero surfaces of said certain selected geometric primitive shapes within said blend and blends,

R_i =variable range defining bounds of said blend and blends,

P_i =implicit function defining said certain selected geometric primitive shapes indexed by i, and

t=thumbweight, a constant which determines a degree of curvature of said blend and blends, and

register means, operatively connected to said central processing means for temporary storage of said geometric primitive shapes and said generated blend and blends from said blend processing means by input and output busses.