Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Efficient polygon-filling algorithms for raster displays
ACM Transactions on Graphics (TOG)
The design and analysis of VLSI circuits
The design and analysis of VLSI circuits
Principles of CMOS VLSI design: a systems perspective
Principles of CMOS VLSI design: a systems perspective
Curve-drawing algorithms for Raster displays
ACM Transactions on Graphics (TOG)
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
Introduction to VLSI Systems
UIST '93 Proceedings of the 6th annual ACM symposium on User interface software and technology
The Discrete Analytical Hyperspheres
IEEE Transactions on Visualization and Computer Graphics
The invisible person: advanced interaction using an embedded interface
EGVE '03 Proceedings of the workshop on Virtual environments 2003
Droplet: a virtual brush model to simulate Chinese calligraphy and painting
Journal of Computer Science and Technology
Virtual hairy brush for painterly rendering
Graphical Models
Model-based analysis of Chinese calligraphy images
Computer Vision and Image Understanding
Technical Section: Realistic synthesis of cao shu of Chinese calligraphy
Computers and Graphics
Mathematical and Computer Modelling: An International Journal
Variable-radius offset curves and surfaces
Mathematical and Computer Modelling: An International Journal
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Brushing commonly refers to the drawing of curves with various line widths in hit-mapped graphics systems. It is best done with circles of suitable diameter so that a constant line width, independent of the curve's slope, is obtained. Allowing all possible integer diameters corresponding to all possible integer line widths results in every second width having an odd value. Thus, the underlying circle algorithm must be able to handle both integer and half-integer radii. Our circle-brush algorithm handles both situations and produces a “best approximation”: All grid points produced simultaneously minimize (1) the residual, (2) the Euclidean distance to the circle, and (3) the displacement along the grid line from the intersection with the circle. Our circle-brush algorithm was developed in careful consideration of its implementation in VLSI.