Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Using program transformations to derive line-drawing algorithms
ACM Transactions on Graphics (TOG)
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Rasterizing curves of constant width
Journal of the ACM (JACM)
Rendering cubic curves and surfaces with integer adaptive forward differencing
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Rasterization of nonparametric curves
ACM Transactions on Graphics (TOG)
GRIP: graphics reduced instruction processor
MICRO 24 Proceedings of the 24th annual international symposium on Microarchitecture
ACM Transactions on Graphics (TOG)
An accurate algorithm for rasterizing algebraic curves
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Robust rendering of general ellipses and elliptical arcs
ACM Transactions on Graphics (TOG)
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
3D scan-conversion algorithms for voxel-based graphics
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
Comparison of viewshed algorithms on regular spaced points
SCCG '02 Proceedings of the 18th spring conference on Computer graphics
Hybrid Scan-Conversion of Circles
IEEE Transactions on Visualization and Computer Graphics
Double-Step Generation of Ellipses
IEEE Computer Graphics and Applications
Arcs: An Efficient Three-Point Arc Algorithm
IEEE Computer Graphics and Applications
3D Line Voxelization and Connectivity Control
IEEE Computer Graphics and Applications
A fast all-integer ellipse discretization algorithm
Graphics programming methods
A fast and simple all-integer parametric line
Graphics programming methods
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Number-theoretic interpretation and construction of a digital circle
Discrete Applied Mathematics
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
Technical section: Drawing lines by uniform packing
Computers and Graphics
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
PACE: polygonal approximation of thick digital curves using cellular envelope
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
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The midpoint method for deriving efficient scan-conversion algorithms to draw geometric curves on raster displays in described. The method is general and is used to transform the nonparametric equation f(x,y) = 0, which describes the curve, into an algorithms that draws the curve. Floating point arithmetic and time-consuming operations such as multiplies are avoided. The maximum error of the digital approximation produced by the algorithm is one-half the distance between two adjacent pixels on the display grid. The midpoint method is compared with the two-point method used by Bresenham, and is seen to be more accurate (in terms of the linear error) in the general case, without increasing the amount of computation required. The use of the midpoint method is illustrated with examples of lines, circles, and ellipses. The considerzations involved in using the method to derive algorithms for drawing more general classes of curves are discussed.