Recent Research Publications

Arc splines

• D. S. Meek and D. J. Walton, "Approximation of discrete data by G¹ arc splines", Computer-Aided Design 24(1992), 301-306.
• D. S. Meek and D. J. Walton, "A note on planar minimax arc splines", Computer & Graphics 16(1992), 431-433.
• D. S. Meek and D. J. Walton, "Approximating quadratic NURBS curves by arc splines", Computer-Aided Design 25(1993), 371-376.
• D. J. Walton and D. S. Meek, "Approximation of quadratic Bézier curves by arc splines", Journal of Computational and Applied Mathematics 54(1994), 107-120.
• M. Yeung and D. J. Walton, "Curve fitting with arc-splines for NC tool path generation", Computer-Aided Design 26(1994), 845-849, .
• D. S. Meek and D. J. Walton, "Approximating smooth planar curves by arc splines", Journal of Computational and Applied Mathematics 59(1995), 221-231.
• D. J. Walton and D. S. Meek, "A planar cubic Bézier spiral", Journal of Computational and Applied Mathematics 72(1996), 85-100.
• D. J. Walton and D. S. Meek, "Approximation of a planar cubic Bézier spiral by circular arcs", Journal of Computational and Applied Mathematics 75(1996), 47-56.
• D. S. Meek and D. J. Walton, "Planar osculating arc splines", Computer Aided Geometric Design 13(1996), 653-671.
• L. Chen, "Generalization of approximation of planar spiral segments by arc splines", M. Sc. thesis, 1998.
• D. S. Meek and D. J. Walton, "Spiral arc spline approximations to a planar spiral", Journal of Computational and Applied Mathematics 107 (1999), 21-30.
• Z. Li and D. S. Meek, "Smoothing an Arc Spline", Computers & Graphics 29 ( 2005), 576-587.
• D. S. Meek and D. J. Walton, "The family of biarcs that matches planar, two-point G1 Hermite data", Journal of Computational and Applied Mathematics 212 (2008), 31-45.
• U. Anant, Shape-preserving Interpolation with Biarcs and NURBS, M. Sc. thesis, May 2010.

Clothoids

• D. S. Meek and D. J. Walton, "The use of Cornu spirals in drawing planar curves of controlled curvature", Journal of Computational and Applied Mathematics 25(1989), 69-78.
• D. J. Walton and D. S. Meek, "Computer aided design for horizontal alignment", ASCE Journal of Transportation Engineering 115(1989), 411-424.
• D. J. Walton and D. S. Meek, "Clothoidal splines", Computers and Graphics 14(1990), 95-100.
• D. S. Meek and D. J. Walton, "Offset curves of clothoidal splines", Computer-Aided Design 22(1990), 199-201.
• D. S. Meek and R. S. D. Thomas, "A guided clothoid spline", Computer Aided Geometric Design 8(1991), 163-174.
• D. S. Meek and D. J. Walton, "Clothoid spline transition spirals", Mathematics of Computation 59(1992), 117-133.
• D. S. Meek and D. J. Walton, "An arc spline approximation to a clothoid", Journal of Computational and Applied Mathematics 170 (2004), 59-77.
• D. S. Meek and D. J. Walton, "A note on finding clothoids", Journal of Computational and Applied Mathematics 170 (2004), 433-453.
• D. J. Walton and D. S. Meek, "A controlled clothoid spline", Computers & Graphics 29 (2005), 353-363.
• D. J. Walton and D. S. Meek, "G¹ interpolation with a single Cornu spiral segment", Journal of Computational and Applied Mathematics 223 (2009), 86-96.

Cubic B-splines and cubic Bezier curves

• D. J. Walton and D. S. Meek, "Curvature bounds for planar B-spline curve segments", Computer-Aided Design 20(1988), 146-150.
• D. S. Meek and D. J. Walton, "Shape determination of planar cubic B-spline segments", Computer-Aided Design 22(1990), 434-441.
• D. J. Walton and D. S. Meek, "Point normal interpolation for stereolithography modelling", Computers and Graphics 19(1995), 345-353.
• D. S. Meek and D. J. Walton, "Geometric Hermite interpolation with Tschirnhausen cubics", Journal of Computational and Applied Mathematics 81(1997), 299-309.
• D. J. Walton and D. S. Meek, "Planar G² transition with a fair cubic Bézier curve", Computer-Aided Design 31(1999), 857-866.
• D. J. Walton, D. S. Meek, and J. M. Ali, "Planar G² transition curves composed of cubic Bézier spiral segments", Journal of Computational and Applied Mathematics 157 (2003), 453-476.

Spirals

• D. S. Meek and R. S. D. Thomas, "Hermite interpolation with a pair of spirals", Computer Aided Geometric Design 10(1993), 491-507.
• D. J. Walton and D. S. Meek, "Interpolation by cubic segments with no local curvature maxima", Cartographica 30(1993), 45-49.
• D. J. Walton and D. S. Meek, "A planar cubic Bézier spiral", Journal of Computational and Applied Mathematics 72(1996), 85-100.
• D. J. Walton and D. S. Meek, "A Pythagorean hodograph quintic spiral", Computer-Aided Design 28(1996), 943-950.
• D. S. Meek and D. J. Walton, "Hermite interpolation with Tschirnhausen cubic spirals", Computer Aided Geometric Design 14(1996), 619-635.
• D. J. Walton and D. S. Meek, "Approximation of a planar cubic Bezier spiral by circular arcs", Journal of Computational and Applied Mathematics 75(1996), 47-56.
• D. J. Walton and D. S. Meek, "Planar G² curve design with spiral segments", Computer-Aided Design 30(1998), 529-538.
• D. S. Meek and D. J. Walton, "Planar spirals that match G² Hermite data", Computer Aided Geometric Design 15(1998), 103-126.
• D. J. Walton and D. S. Meek, "G² curves composed of planar cubic and Pythagorean hodograph quintic spirals", Computer Aided Geometric Design 15(1998), 547-566.
• D. S. Meek and D. J. Walton, "Planar G¹ Hermite interpolation with spirals", Computer Aided Geometric Design 15(1998), 787-801.
• D. S. Meek and D. J. Walton, "Spiral arc spline approximations to a planar spiral", Journal of Computational and Applied Mathematics 107 (1999), 21-30.
• D. J. Walton and D. S. Meek, "A generalisation of the Pythagorean Hodograph quintic spiral", Journal of Computational and Applied Mathematics 172 (2004), 271-287.
• T. N. T. Goodman and D. S. Meek, "Planar interpolation with a pair of rational spirals", Journal of Computational and Applied Mathematics 201 (2007), 112-127.
• D. J. Walton and D. S. Meek, "G² curve design with a pair of Pythagorean hodograph quintic spiral segments", Computer Aided Geometric Design 24 (2007), 267-285.
• Z. Li, L. Z. Ma, and D. S. Meek, "Rational quadratic B-spline curves with monotone curvature", Journal of Information & Computational Science 4: 1 (2007), 119-127.
• D. J. Walton, D. S. Meek, "An Improved Euler Spiral Algorithm for Shape Completion", 2008 Canadian Conference on Computer and Robot Vision, Windsor, Ontario, May 2008, 237-244.
• D. S. Meek and D. J. Walton, "A two-point G¹ Hermite interpolating family of spirals", Journal of Computational and Applied Mathematics 223 (2009), 97-113.
• T. N. T. Goodman, D. S. Meek, and D. J. Walton, "An involute spiral that matches G² Hermite data in the plane", Computer Aided Geometric Design 26 (2009), 733-756.

Other curves

• D. J. Walton and D. S. Meek, "Curvature extrema of planar parametric cubic curves", Journal of Computational and Applied Mathematics 134 (2001), 69-83.
• D. J. Walton and D. S. Meek, "Planar G² transition with a fair Pythagorean hodograph quintic curve", Journal of Computational and Applied Mathematics 138 (2002), 109-126.
• D. S. Meek and D. J. Walton, "Planar G² Hermite interpolation with some fair, C-shaped curves", Journal of Computational and Applied Mathematics 139 (2002), 141-161.
• D. S. Meek, "Coaxing a planar curve to comply", Journal of Computational and Applied Mathematics 140 (2002), 599-618.
• D. S. Meek, B. H. Ong, and D. J. Walton, "A constrained guided G¹ continuous spline curve", Computer-Aided Design 35 (2003), 591-599.
• D. S. Meek, B. H. Ong, and D. J. Walton, "Constrained interpolation with rational cubics", Computer Aided Geometric Design 21 (2003), 253-275.
• Z. Li, D. S. Meek, D. J. Walton, "A smooth, obstacle-avoiding curve", Computers & Graphics 30 ( 2006), 581-587.
• Z. Li, L. Z. Ma, and D. S. Meek, "Reconstruction of G² transition curve for two separated circular arcs" (in Chinese), Journal of Computer-Aided Design and Computer Graphics 18 (2006), 265-269.
• Z. Li, D. S. Meek, D. J. Walton, "A smooth, obstacle-avoiding curve", Computers & Graphics 30 (2006), 581-587.
• D. S. Meek and D. J. Walton, "Blending two parametric curves", Computer-Aided Design 41 (2009), 423-431.
• D. J. Walton and D. S. Meek, "G² blends of linear segments with cubics and Pythagorean-hodograph quintics", International Journal of Computer Mathematics 86 (2009), 1498-1511.

Surfaces and 3D modelling

• M. Yeung, "Three dimensional object modeling from planar sections", M.Sc. thesis, 1992.
• D. J. Walton and M. Yeung, "Geometric modelling from CT scans for Stereolithography Apparatus", CAD / Graphics '93 Conference, Beijing, China, 1993.
• D. J. Walton and D. S. Meek, "Point normal interpolation for stereolithography modelling", Computers and Graphics, 19(1995), 345-353.
• D. J. Walton and D. S. Meek, "A triangular G¹ Bézier patch from boundary curves", Computer-Aided Design 28(1996), 113-123.
• D. S. Meek and D. J. Walton, "Comparison of smooth polynomial functional surfaces for use in alignment", Image and Vision Computing 15(1997), 529-534.
• C. Li, "Wavelets and the use of curvature to approximate surfaces", M. Sc. thesis, 1997.
• D. S. Meek and D. J. Walton, "On surface normal and Gaussian curvature approximations given data sampled from a smooth surface", Computer Aided Geometric Design 17(2000), 521-543.

Visualization

• M.M. Madi and D.J. Walton, Preserving special features on 3D Object representation during surface smoothing, WSCG'99 (The 7th International Conference in Central Europe on Computer Graphics, Visualization and Interactive Digital Media, February 8-12, 1999).
• M. Madi and D.J. Walton, Visualisation of layered objects, Computers & Graphics 23(3), 1999, 331-342.
• M. Madi, "Surface segmentation and shape modification for 3D geometric objects", Ph. D. thesis, 2000.
• M. Madi and D.J. Walton, From Hierarchical Structures to Triangular-Loop Structures: A Representation Transformation Algorithm, SCCG 2000 (Spring Conference on Computer Graphics, Budmerice Castle, Slovak Republic, May 4-6, 2000), 246-251.
• T. Nowicki, Global Illumination and Approximating Reflectance in Real-Time, M. Sc. thesis, March 2007.

Unclassified

• D. S. Meek and D. J. Walton, "Several methods for representing discrete data by line segments", Cartographica 28(1991), 13-20.
• D. J. Walton and R. Xu, "Representation of contour lines by turning point preserving quadratic splines", The Cartographic Journal, 28, 208-212, 1991.
• D. J. Walton and R. Xu, "Turning point preserving planar interpolation", ACM Transactions on Graphics, 10, 297-311, 1991.
• D. J. Walton and C. Wu, "Axis location of a worn cylindrical mechanical object", Computer-Aided Design, 24(1992), 258-266.
• S. Kalynuk, "The application of edge detection and edge tracking algorithms to the determination of tree ring properties", M. Sc. thesis, 1993.
• R.L. Zhang, D.J. Walton and W.D. Hoskins, Prediction of natural gas consumption, IEEE Canadian Conference on Electrical and Computer Engineering, Vancouver,1993.
• D. S. Meek and D. J. Walton, "Alignment of planar curves", Image and Vision Computing 12(1994), 305-311.
• M. Wirth, "Registration of Medical Images: Methods of Point Matching by Geometric Transformation", M. Sc. thesis, 1994.
• T. Lambert. "Empty-shape Triangulation Algorithms", Ph. D. thesis, 1994.
• P. Wong, "Application of Ray Tracing and Constrained Tesselations to Boreal Tree Growth Simulation", M. Sc. thesis, 1996.
• F. Jahan and D.J. Walton, "Texture analysis of osteoporotic bone scan images vs. normal bone scan images", Proc. Ninth IASTED International Conference on Visualization, Imaging, and Image Processing, Cambridge, United Kingdom, 13-15 July 2009, 1-6.