Fairing Be´zier curves with constraints
Computer Aided Geometric Design
Sculpting: an interactive volumetric modeling technique
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Geometric concepts for geometric design
Geometric concepts for geometric design
SKETCH: an interface for sketching 3D scenes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Interpolating curve with B-spline curvature function
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
A shape controlled fitting method for Be´zier curves
Computer Aided Geometric Design
Teddy: a sketching interface for 3D freeform design
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
Applied Geometry for Computer Graphics
Applied Geometry for Computer Graphics
Image Processing Handbook, Fourth Edition
Image Processing Handbook, Fourth Edition
A New Aesthetic Dsign Workflow - Results from the European Project FIORES
CAD Tools and Algorithms for Product Design [Dagstuhl Seminar, November 1998]
Freehand Sketch System for 3D Geometric Modeling
SMA '97 Proceedings of the 1997 International Conference on Shape Modeling and Applications (SMA '97)
Target curvature driven fairing algorithm for planar cubic B-spline curves
Computer Aided Geometric Design
Practical Linear Algebra: A Geometry Toolbox
Practical Linear Algebra: A Geometry Toolbox
Learning Design with Alias StudioTools: A Hands-on Guide to Modeling and Visualization in 3D (Official Alias Training Guide)
Quintic B-spline curve generation and modification based on specified radius of curvature
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
WSEAS Transactions on Mathematics
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Image processing techniques are used to detect the edges of a hand-drawn sketch. Generally, various types of gradation are expressed in the background of a hand-drawn sketch. Therefore, the original image is transformed into a logarithmic image. The entire image has to be binarized for edge detection. To smooth the edge of the binary image, feature based erosion and dilation is applied. A Laplacian operation is applied to the binary image to detect the edge in the binary image. This edge position corresponds to the position of the line in the hand-drawn sketch image. Line segments which represent the detected edges are generated. Using the positions and gradients on the line segments, a NURBS curve is generated. The shape of the NURBS curve extracted from the sketch image is examined by the designer visually. The shape of this NURBS curve generally coincides with the intention of the designer, but does not coincide precisely. Therefore, a curve shape modification method based on the specified radius of curvature is applied. The sum of the squared differences between the radius of curvature of a curve and the specified radius of curvature of an entire curve is linearized by Taylor's theorem, then minimized. The specification of radius of curvature is performed by selecting a predefined fair NURBS curve using the similarity of radius of curvature distribution. Examples of NURBS curve generation based on a hand-drawn sketch are given according to the generation process.