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at those curves as the surfaces to be joined, leading to creases in the joined surface along those curves. To fix this problem, the linear interpolation can be replaced with
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Although the bilinear Coons patch exactly meets its four boundary curves, it does not necessarily have the same
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with the weights chosen to match the partial derivatives at the corners. This forms a
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638:{\displaystyle B(s,t)=c_{0}(0)(1-s)(1-t)+c_{0}(1)s(1-t)+c_{1}(0)(1-s)t+c_{1}(1)st.}
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Surfaces for
Computer-Aided Design of Space Forms, MAC-TR-41
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763:{\displaystyle C(s,t)=L_{c}(s,t)+L_{d}(s,t)-B(s,t).}
762:
637:
423:{\displaystyle L_{d}(s,t)=(1-s)d_{0}(t)+sd_{1}(t)}
422:
300:{\displaystyle L_{c}(s,t)=(1-t)c_{0}(s)+tc_{1}(s)}
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444:on the four corner points is another surface
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63:, to mesh problem domains into elements.
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186:can be used to interpolate between
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788:bicubically blended Coons patch
854:"Surface Construction Schemes"
829:Coons, Steven A. (June 1967).
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650:bilinearly blended Coons patch
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66:Coons patches are named after
55:applications, particularly in
1:
126:) which meet at four corners
437:defined on the unit square.
903:
882:Multivariate interpolation
835:. Cambridge, MA: MIT/LCS
61:boundary element method
53:computational mechanics
47:to smoothly join other
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442:bilinear interpolation
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887:Splines (mathematics)
784:cubic Hermite splines
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57:finite element method
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184:linear interpolation
70:, and date to 1967.
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68:Steven Anson Coons
22:
20:Sample Coons patch
74:Bilinear blending
51:together, and in
45:computer graphics
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856:. Archived from
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805:Atlas (topology)
774:Bicubic blending
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652:is the surface
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41:parametrization
32:, is a type of
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435:ruled surfaces
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860:on 2010-08-06
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810:Interpolation
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780:tangent plane
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34:surface patch
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862:. Retrieved
858:the original
852:Weiqing Gu.
850:
837:. Retrieved
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318:
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310:and between
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29:
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78:Given four
30:Coons patch
26:mathematics
876:Categories
816:References
200:, that is
737:−
593:−
556:−
516:−
501:−
368:−
245:−
864:6 August
794:See also
49:surfaces
43:used in
38:manifold
800:Surface
82:curves
839:2 June
175:(1) =
161:(0) =
147:(1) =
133:(0) =
182:(1);
168:(1),
154:(0),
140:(0),
80:space
866:2010
841:2024
440:The
193:and
59:and
28:, a
115:),
104:),
93:),
36:or
24:In
878::
790:.
648:A
317:,
868:.
843:.
758:.
755:)
752:t
749:,
746:s
743:(
740:B
734:)
731:t
728:,
725:s
722:(
717:d
713:L
709:+
706:)
703:t
700:,
697:s
694:(
689:c
685:L
681:=
678:)
675:t
672:,
669:s
666:(
663:C
633:.
630:t
627:s
624:)
621:1
618:(
613:1
609:c
605:+
602:t
599:)
596:s
590:1
587:(
584:)
581:0
578:(
573:1
569:c
565:+
562:)
559:t
553:1
550:(
547:s
544:)
541:1
538:(
533:0
529:c
525:+
522:)
519:t
513:1
510:(
507:)
504:s
498:1
495:(
492:)
489:0
486:(
481:0
477:c
473:=
470:)
467:t
464:,
461:s
458:(
455:B
418:)
415:t
412:(
407:1
403:d
399:s
396:+
393:)
390:t
387:(
382:0
378:d
374:)
371:s
365:1
362:(
359:=
356:)
353:t
350:,
347:s
344:(
339:d
335:L
322:1
319:d
315:0
312:d
295:)
292:s
289:(
284:1
280:c
276:t
273:+
270:)
267:s
264:(
259:0
255:c
251:)
248:t
242:1
239:(
236:=
233:)
230:t
227:,
224:s
221:(
216:c
212:L
198:1
195:c
191:0
188:c
180:1
177:d
173:1
170:c
166:0
163:d
159:1
156:c
152:1
149:d
145:0
142:c
138:0
135:d
131:0
128:c
124:t
122:(
120:1
117:d
113:t
111:(
109:0
106:d
102:s
100:(
98:1
95:c
91:s
89:(
87:0
84:c
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
