로그인

검색

조회 수 3615 추천 수 0 댓글 0
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 게시글 수정 내역 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 게시글 수정 내역 댓글로 가기 인쇄

http://www.algorithmist.net/technotes.html

 

Computational Geometry

Focusing primarily on interactive creation and display of two-dimensional curves, I hope this series illustrates that Flash is a valuable tool in teaching computational geometry. Each TechNote below opens in a new browser window.

:: Natural Cubic Splines - Natural and parametric cubic splines.

:: Hermite Curves - Cubic Hermite curves.

:: Quadratic Beizer Curves - Quadratic Beizer's and MovieClip.curveTo().

:: Cubic Bezier Curves - Cubic Bezier's and introduction to quadratic approximation.

:: Catmull-Rom Splines - An introduction to Catmull-Rom Splines.

:: Arc Length of a Catmull-Rom Spline - Arc Length of parametric curves and derivative evaluation, applied to Catmull-Rom splines.

:: Curve-Constrained Scrolling Via Script - Parametric Quadratic and Piecewise Hermite curves applied to curve-constrained scroll indicators.

:: Arc-Length Parameterization - Introduction to curve parameterization and how to reparameterize a curve on arc length. Techniques applied to a Catmull-Rom spline. Examples include how to distribute sprites evenly along a curve and path animation (including path following and orientation).

:: Recursive Subdivision - Splitting a cubic Bezier curve into multiple equivalent, but smaller segments. Several subdivision approaches are discussed with the ultimate goal of pairing a fast subdivision with a piecewise cubic Bezier spline.

:: Composite Bezier Curves - Constructing a piecewise cubic Bezier curve that interpolates a set of knots with G-1 continuity and tension control. Optimized for fast drawing.

Online Demos

These interactive demos illustrate various concepts in applied mathematics. Most initial examples are from the field of computational geometry. All demos required the Flash 9 player.

:: Parameterization Demo - Illustrate the difference bewteen uniform and arc-length parameterization on a cubic Bezier spline.

::Quadratic Bezier Parameterization - illustrates the difference in natural vs arc-length parameterization for a simple quadratic Bezier curve.

::Quad. Bezier, 3-point interpolation - The classic formula familiar to many Flash programmers is actually a simplified version of a more general parameterization, called 'midpoint' parameterization or 'midpoint interpolation'. The more general formula is discussed in the Cubic Bezier TechNote. This demo illustrates the difference between midpoint, chord-length, and arbitrary parameterizations.

::Catmull-Rom Spline animation - a simple example illustrating the animation of a Catmull-Rom spline from beginning to end, as if it were being drawn by hand. Also a subtle introduction to spline parameterization.

::Closed-Loop Catmull-Rom spline - a simple method for setting outer control points for a smooth, continuous-loop Catmull-Rom spline.

::Path Animation with Papervision 3D - a simple demo illustrating path animation with Papervision 3D and the 3D Catmull-Rom spline.

::Lemniscate of Bernoulli - how to use a closed-loop Catmull-Rom spline to animate sprites around a Lemniscate of Bernoulli (infinity or fiture-8 shape).

::Papervision 3D Figure-8's- builds upon the 2D Lemniscate of Bernoulli example to animate markers along figure-8 paths in the XY, XZ, and YZ planes.

::Papervision 3D Path Animation from 3ds max - uses spline data exported from 3ds max (in XML) and the Singularity 3D Bezier spline for path animation in Papervision 3D.

::Quadratic Bezier y at x - computes (t,y) values along a quadratic Bezier curve at a given x-coordinate.

::Cubic Bezier y at x - computes (t,y) values along a cubic Bezier curve at a given x-coordinate.

::Closest Point on Cubic - closest point on a cubic Bezier to an arbitrary point (port of class Graphic Gem algorithm).

::Closest Point on Quadratic - closest point on a quadratic Bezier to an arbitrary point (Graphic Gem algorithm generalized to work with quads or cubics).

::Easing Along a Cubic Bezier Curve- Penner easing functions applied to easing along a parametric curve. Another practical application of arc-length parameterization.

::Cubic Bezier 4-point Interpolation-Interpolating four points with a cubic Bezier curve.

?

List of Articles
번호 분류 제목 글쓴이 날짜 조회 수
393 IT 비회원 글쓰기 시 스팸 방지 MoA 2013.09.26 53566
392 IT 인텔 모바일 CPU 호환성 가이드(Intel Mobile Processor Compatibility Guide) - CPU 업그레이드 관련 1 모아레 2010.09.16 7365
391 IT 공유기 문제 관련 모아레 2008.03.11 5006
390 IT Google analytics 등의 분석 툴에서 간혹 방문 시간이 0초로 표시되는 이유 MoA 2013.11.30 4898
389 IT 노트북 배터리에 대한 모든 것 (스크롤 압박 주의) 모아레 2009.02.07 4682
388 교양 해외 여행 시 주의해야할 나라별 문화차이 1 너울 2012.12.23 4452
387 IT 아이폰4 카메라 vs 니콘 D40 비교 너울 2011.08.29 4436
386 과학 수학 기호 MoA 2007.04.19 4353
385 IT 페이스북 '알만한 사람' 어떻게 알아낼까? Naya 2011.11.26 4237
384 IT ATIV 프리뷰 Naya 2012.09.25 4231
383 IT Google Project Glass: One day... Naya 2012.04.07 4175
382 IT 구글 포토 사진 날짜 변경 방법 MoA 2015.08.07 4159
381 교양 속독법의 원리 모아레 2010.03.09 4091
380 IT openfire (메신저 서버) 설치하기 MoA 2013.01.18 4077
379 IT 애플워치 클락콜로지(clockology) 설정방법 정리 OBG 2024.11.07 4065
378 IT 리눅스를 처음 사용하시는 분들을 위한 북마크 모아레 2008.05.12 3847
377 IT How does Facebook generate the list of friend icons on the left side? 비지 2011.05.30 3819
376 IT iOS 5’s Seven New Hidden Features Naya 2011.10.18 3779
375 IT 네이버, 노무현을 지우다 Naya 2012.04.15 3714
374 IT 브라우저별 HTML 5 Test 비지 2011.05.02 3683
Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 ... 20 Next
/ 20