Connected Minimal Acceleration Trigonometric Curves

Tony Barrera
Barrera Kristiansen AB

Anders Hast
Creative Media Lab, University of Gävle, Sweden

Ewert Bengtsson
Centre for Image Analysis, Uppsala University, Sweden

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Ingår i: SIGRAD 2005 The Annual SIGRAD Conference Special Theme - Mobile Graphics

Linköping Electronic Conference Proceedings 16:1, s. 1-5

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Publicerad: 2005-11-23


ISSN: 1650-3686 (tryckt), 1650-3740 (online)


We present a technique that can be used to obtain a series of connected minimal bending trigonometric splines that will intersect any number of predefined points in space. The minimal bending property is obtained by a least square minimization of the acceleration. Each curve segment between two consecutive points will be a trigonometric Hermite spline obtained from a Fourier series and its four first terms. The proposed method can be used for a number of points and predefined tangents. The tangent length will then be optimized to yield a minimal bending curve. We also show how both the tangent direction and length can be optimized to give as smooth curves as possible. It is also possible to obtain a closed loop of minimal bending curves. These types of curves can be useful tools for 3D modelling; etc.


Trigonometric curves; Hermite curves; least square minimization


V. ALBA-FERNANDEZ; M.J. IBANEZ-PEREZ; M.D. JIMENEZGAMERO 2004. A Bootstrap Algorithm for the Two-Sample Problem Using Trigonometric Hermite Spline Interpolation Communications in Nonlinear Science and Numerical Simulation. Vol. 9. Num. 2. Pag. 275-286

T. BARRERA; A. HAST; E. BENGTSSON 2005. Minimal Acceleration Hermite Curves Graphics Programming Gems V; Charles River Media; Edited by Kim Pallister; pp 225-231.

R.H. BARTELS; J.C. BEATTY;AND B.A. BARSKY 1998. An Introduction to. Splines for use in Computer Graphics and. Geometric Modeling ”Hermite and Cubic Spline Interpolation.” Ch. 3; pp. 9-17.

R. L. BURDEN; J.D. FAIRES 1989. Numerical Analysis Numerical Analysis; PWS-KENT Publishing company Boston; pp. 439; 440.

E. CATMULL; R. ROM 1974. A Class of Local Interpolating Splines Computer Aided Geometric design; pp. 317-326.

A. FOLEY; J. D.; ET AL 1997. Computer Graphics: Principles and Practice; 2nd ed. Addison-Wesley; p. 480.

X. HAN 2003. Piecewise Quadratic Trigonometric Polynomial Curves Mathematics of Computation; pp. 1369-1377.

D. HEARN; M.P BAKER 2004. Computer Graphics with OpenGL Pearson Education Inc.; pp. 426-429.

E. LENGYEL. 2004. E. Lengyel; Mathematics for 3D Game Programming and Computer Graphics; 2nd ed. E. Lengyel; Charles River Media; pp. 433-436.

T. LYCHE. 1979. A Newton form for Trigonometric Hermite Interpolation

E. Lengyel; Charles River Media; pp. 433-436.

PRESS ET AL. 1992. Numerical Recipes in C. [Press92] Cambridge University Press; pp. 74-75.

I. J. SCHOENBERG 1964. On Trigonometric Spline Interpolation Journal of Mathematics and Mechanics; pp. 795-825.

A. VLACHOS; J ISIDORO Smooth C2 Quaternion-based Flythrough Paths Game Programming Gems 2; Charles River Media; Edited by Mark Deloura; pp. 220-227.

G. WALZ Identities for Trigonometric B-Splines with an Application to Curve Design Identities for trigonometric B-splines with an application to curve design. BIT 37; pp. 189-201.

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