Constrained Visualization Using the Shepard Interpolation Family

This paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data are inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be const...

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Published in:	Computer graphics forum Vol. 24; no. 4; pp. 809 - 820
Main Authors:	Brodlie, K. W., Asim, M. R., Unsworth, K.
Format:	Journal Article
Language:	English
Published:	9600 Garsington Road , Oxford , OX4 2DQ , UK Blackwell Publishing Ltd 01.12.2005
Subjects:	Computer graphics constraints G.1.1 Numerical Analysis: Interpolation G.1.6 Numerical Analysis: Optimization I.3.5 Computer Graphics-Computational Geometry and Object Modelling Interpolation positivity shape preservation Shepard's method Studies visualisation Visualization
ISSN:	0167-7055, 1467-8659
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Abstract	This paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data are inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be constrained to preserve positivity. We do this by forcing the quadratic basis functions to be positive. The method can be extended to handle other types of constraints, including lower bound of 0 and upper bound of 1—as occurs with fractional data. A further extension allows general range restrictions, creating an interpolant that lies between any two specified functions as the lower and upper bounds.
AbstractList	This paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data are inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be constrained to preserve positivity. We do this by forcing the quadratic basis functions to be positive. The method can be extended to handle other types of constraints, including lower bound of 0 and upper bound of 1—as occurs with fractional data. A further extension allows general range restrictions, creating an interpolant that lies between any two specified functions as the lower and upper bounds. This paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data are inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be constrained to preserve positivity. We do this by forcing the quadratic basis functions to be positive. The method can be extended to handle other types of constraints, including lower bound of 0 and upper bound of 1 - as occurs with fractional data. A further extension allows general range restrictions, creating an interpolant that lies between any two specified functions as the lower and upper bounds. [PUBLICATION ABSTRACT]
Author	Unsworth, K. Asim, M. R. Brodlie, K. W.
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References	B. Mulansky and J. Schmidt. Powell-Sabin splines in range restricted interpolation of scattered data. Computing, 53(1994), 137-154. Y. Xiao and C. Woodbury. Constraining global interpolation methods for sparse data volume visualization. International Journal of Computers and Applications, 21, 2 (1999), 59-64. R. J. Renka. Algorithm 660: QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data. ACM Transactions on Mathematical Software 14, 2 (1988), 149-150. M. Asim and K. Brodlie. Curve drawing subject to positivity and more general constraints. Computers and Graphics, 27(2003), 469-485. E. Chan and B. Ong. Range restricted scattered data interpolation using convex combination of cubic Bezier triangles. Journal of Computational and Applied Mathematics, 136(2001), 135-147. W. J. Gordon and J. A. Wixom. Shepard's method of metric interpolation to bivariate and multivariate interpolation. Mathematics of Computation, 32, 141 (1978), 253-264. R. Fletcher. Practical Methods of Optimization. Wiley, Chichester and New York , 1987. P. Lancaster and K. Salkauskas. Curve and Surface Fitting: An Introduction. Academic Press, London , 1986. R. Franke and G. Nielson. Smooth interpolation of large sets of scattered data. International Journal of Numerical Methods in Engineering, 15(1980), 1691-1704. G. M. Nielson. Scattered data modelling. IEEE Computer Graphics and its Applications, (1993), 60-70. R. J. Renka. Multivariate interpolation of large sets of scattered data. ACM Transactions on Mathematical Software, 14, 2 (1988), 139-148. G. Nielson. The side-vertex method for interpolation in triangles. Journal of Approximation Theory, 25(1979), 318-336. F. I. Utreras. Positive thin plate splines. J. Approximation Theory and its Applications, 1, 3 (1985), 77-108. R. Barnhill G. Birkhoff and W. Gordon. Smooth interpolation in triangles. Journal of Approximation Theory, 8(1973), 114-128. 1980; 15 1985; 1 1979; 25 2000 1978; 32 1988; 14 1987 1986 1996 2003; 27 1999; 21 2005 1993 1973; 8 2001; 136 1968 1994; 53 1977 e_1_2_8_16_2 e_1_2_8_17_2 e_1_2_8_18_2 e_1_2_8_19_2 Xiao Y. (e_1_2_8_11_2) 1999; 21 e_1_2_8_12_2 e_1_2_8_13_2 e_1_2_8_14_2 e_1_2_8_15_2 e_1_2_8_9_2 Asim M. (e_1_2_8_3_2) 2000 e_1_2_8_2_2 Utreras F. I. (e_1_2_8_10_2) 1985; 1 e_1_2_8_4_2 e_1_2_8_5_2 Fletcher R. (e_1_2_8_20_2) 1987 e_1_2_8_8_2 e_1_2_8_7_2 e_1_2_8_21_2 Ong B. (e_1_2_8_6_2) 1996 Lancaster P. (e_1_2_8_22_2) 1986
References_xml	– reference: R. Franke and G. Nielson. Smooth interpolation of large sets of scattered data. International Journal of Numerical Methods in Engineering, 15(1980), 1691-1704. – reference: M. Asim and K. Brodlie. Curve drawing subject to positivity and more general constraints. Computers and Graphics, 27(2003), 469-485. – reference: F. I. Utreras. Positive thin plate splines. J. Approximation Theory and its Applications, 1, 3 (1985), 77-108. – reference: R. J. Renka. Algorithm 660: QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data. ACM Transactions on Mathematical Software 14, 2 (1988), 149-150. – reference: R. Barnhill G. Birkhoff and W. Gordon. Smooth interpolation in triangles. Journal of Approximation Theory, 8(1973), 114-128. – reference: B. Mulansky and J. Schmidt. Powell-Sabin splines in range restricted interpolation of scattered data. Computing, 53(1994), 137-154. – reference: Y. Xiao and C. Woodbury. Constraining global interpolation methods for sparse data volume visualization. International Journal of Computers and Applications, 21, 2 (1999), 59-64. – reference: R. J. Renka. Multivariate interpolation of large sets of scattered data. ACM Transactions on Mathematical Software, 14, 2 (1988), 139-148. – reference: E. Chan and B. Ong. Range restricted scattered data interpolation using convex combination of cubic Bezier triangles. Journal of Computational and Applied Mathematics, 136(2001), 135-147. – reference: R. Fletcher. Practical Methods of Optimization. Wiley, Chichester and New York , 1987. – reference: W. J. Gordon and J. A. Wixom. Shepard's method of metric interpolation to bivariate and multivariate interpolation. Mathematics of Computation, 32, 141 (1978), 253-264. – reference: P. Lancaster and K. Salkauskas. Curve and Surface Fitting: An Introduction. Academic Press, London , 1986. – reference: G. Nielson. The side-vertex method for interpolation in triangles. Journal of Approximation Theory, 25(1979), 318-336. – reference: G. M. Nielson. Scattered data modelling. IEEE Computer Graphics and its Applications, (1993), 60-70. – year: 1986 – volume: 1 start-page: 77 issue: 3 year: 1985 end-page: 108 article-title: Positive thin plate splines publication-title: J. Approximation Theory and its Applications – volume: 14 start-page: 149 issue: 2 year: 1988 end-page: 150 article-title: Algorithm 660: QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data publication-title: ACM Transactions on Mathematical Software – volume: 21 start-page: 59 issue: 2 year: 1999 end-page: 64 article-title: Constraining global interpolation methods for sparse data volume visualization publication-title: International Journal of Computers and Applications – year: 2005 – volume: 27 start-page: 469 year: 2003 end-page: 485 article-title: Curve drawing subject to positivity and more general constraints publication-title: Computers and Graphics – start-page: 259 year: 1996 end-page: 274 – start-page: 60 year: 1993 end-page: 70 article-title: Scattered data modelling publication-title: IEEE Computer Graphics and its Applications – volume: 25 start-page: 318 year: 1979 end-page: 336 article-title: The side‐vertex method for interpolation in triangles publication-title: Journal of Approximation Theory – year: 1987 – start-page: 69 year: 1977 end-page: 120 – volume: 14 start-page: 139 issue: 2 year: 1988 end-page: 148 article-title: Multivariate interpolation of large sets of scattered data publication-title: ACM Transactions on Mathematical Software – volume: 15 start-page: 1691 year: 1980 end-page: 1704 article-title: Smooth interpolation of large sets of scattered data publication-title: International Journal of Numerical Methods in Engineering – year: 2000 – start-page: 189 year: 2000 end-page: 230 – volume: 32 start-page: 253 issue: 141 year: 1978 end-page: 264 article-title: Shepard's method of metric interpolation to bivariate and multivariate interpolation publication-title: Mathematics of Computation – volume: 8 start-page: 114 year: 1973 end-page: 128 article-title: Smooth interpolation in triangles publication-title: Journal of Approximation Theory – volume: 53 start-page: 137 year: 1994 end-page: 154 article-title: Powell‐Sabin splines in range restricted interpolation of scattered data publication-title: Computing – volume: 136 start-page: 135 year: 2001 end-page: 147 article-title: Range restricted scattered data interpolation using convex combination of cubic Bezier triangles publication-title: Journal of Computational and Applied Mathematics – start-page: 517 year: 1968 end-page: 523 – volume-title: Visualization of data subject to positivity constraint year: 2000 ident: e_1_2_8_3_2 – ident: e_1_2_8_2_2 – ident: e_1_2_8_21_2 – ident: e_1_2_8_12_2 doi: 10.1145/800186.810616 – ident: e_1_2_8_15_2 doi: 10.1109/38.180119 – ident: e_1_2_8_7_2 doi: 10.1016/0021-9045(79)90020-0 – volume-title: Practical Methods of Optimization year: 1987 ident: e_1_2_8_20_2 – ident: e_1_2_8_9_2 doi: 10.1016/S0377-0427(00)00580-X – volume: 21 start-page: 59 issue: 2 year: 1999 ident: e_1_2_8_11_2 article-title: Constraining global interpolation methods for sparse data volume visualization publication-title: International Journal of Computers and Applications – ident: e_1_2_8_5_2 doi: 10.1016/S0097-8493(03)00084-0 – ident: e_1_2_8_17_2 doi: 10.1145/45054.45055 – volume: 1 start-page: 77 issue: 3 year: 1985 ident: e_1_2_8_10_2 article-title: Positive thin plate splines publication-title: J. Approximation Theory and its Applications – ident: e_1_2_8_8_2 doi: 10.1007/BF02252986 – ident: e_1_2_8_13_2 doi: 10.1002/nme.1620151110 – ident: e_1_2_8_14_2 doi: 10.1016/B978-0-12-587260-7.50008-X – ident: e_1_2_8_19_2 doi: 10.2307/2006273 – ident: e_1_2_8_4_2 doi: 10.1016/0021-9045(73)90020-8 – start-page: 259 volume-title: Advanced Topics in Multivariate Approximation year: 1996 ident: e_1_2_8_6_2 – ident: e_1_2_8_16_2 doi: 10.1145/45054.356231 – volume-title: Curve and Surface Fitting: An Introduction year: 1986 ident: e_1_2_8_22_2 – ident: e_1_2_8_18_2
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SubjectTerms	Computer graphics constraints G.1.1 Numerical Analysis: Interpolation G.1.6 Numerical Analysis: Optimization I.3.5 Computer Graphics-Computational Geometry and Object Modelling Interpolation positivity shape preservation Shepard's method Studies visualisation Visualization
Title	Constrained Visualization Using the Shepard Interpolation Family
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