# Fast Approximative Arc

## Fast Approximative Arc

*Note : these versions are superseded by the Fast & Accurate Arc algorithm*

This algorithm draws

**Arcs**(partial circles) in the GRAPH PICTure,

using an approximative "circumference length" code.

The result can sometimes be wrong by one pixel.

**Input**:

5 : X0 (pixel coordinate, 0 is first left column, can be negative)

4 : Y0 (pixel coordinate, 0 is first up line, can be negative)

3 : Radius (pixel, maximum 60)

2 : Start Bearing (degree, 0° is North (up))

1 : End Bearing (degree, 0° is North (up))

Fast Approximative Arc V1.0, for HP48 & HP49/50

Benchmark results, using an HP48SX

(expect later model to perform better) :

30 pixels radius

Full : 0.50s

Half : 0.29s

Quarter : 0.18s

Eight : 0.12s

1° : 0.07s (Note : 0° means "Full Circle")

Source Code, V1.0

Last edited by Admin on Fri 15 Aug - 3:17; edited 1 time in total

## Cyrille de Brebisson - Very fast Arc algorithm

Introducing an MASD code proposed by

Cyrille de Brebisson's Arc Toolbox v1.1 : HP48 S/G Binary (1651 Bytes) (Checksum #477Bh)

Source Code, 99.9% hand-made by Cyrille (only header is adapted)

6 : Grob ( Optional, will draw in Graphic Area if none provided )

5 : X0

4 : Y0

3 : Radius

2 : Start Bearing (°)

1 : End Bearing (°)

(0,0) is upper left.

0° is North. Bearing values must be

X0 & Y0 must be

All values are limited to 2047 (Grob Width/Height, X, Y & Radius)

This code is

At the time of this writing, this is the fastest code around.

This code is still based on "pixel counting" approximation,

however this new version has a particularly good algorithm,

resulting in near perfect accuracy as long as R<255.

Above this range, a small inaccuracy of a few pixels (at most) can be witnessed.

30pixels half circle : starts one pixel late, ends correctly

100pixels 3/4 circle : starts one pixel late, ends correctly

Cyrille de Brebisson's Arc Toolbox V1.0 : HP48 S/G Binary (1215 Bytes)

with Source Code

__to draw Arcs.__**Cyrille de Brebisson**Cyrille de Brebisson's Arc Toolbox v1.1 : HP48 S/G Binary (1651 Bytes) (Checksum #477Bh)

Source Code, 99.9% hand-made by Cyrille (only header is adapted)

__Input__:6 : Grob ( Optional, will draw in Graphic Area if none provided )

5 : X0

4 : Y0

3 : Radius

2 : Start Bearing (°)

1 : End Bearing (°)

*Notes*:(0,0) is upper left.

0° is North. Bearing values must be

__positive__.X0 & Y0 must be

__positive__(*Warning : you risk a reset if you don't respect this rule*)All values are limited to 2047 (Grob Width/Height, X, Y & Radius)

This code is

**fast, as can be shown in following benchmarks :***extremely*Name | Input | HP48SX | HP48GX | HP50G |

30pixels, Quarter circle | X=65,Y=32,R=30,S=90,E=180 | 30ms | ||

30pixels, Half circle | X=65,Y=32,R=30,S=90,E=270 | 31ms | ||

30pixels, Full circle | X=65,Y=32,R=30,S=90,E=90 | 34ms | ||

60pixels, Full circle | X=30,Y=0,R=60,S=90,E=90 | 56ms | ||

150pixels, 3/4 circle | X=65,Y=160,R=150,S=90,E=360 | 89ms |

This code is still based on "pixel counting" approximation,

however this new version has a particularly good algorithm,

resulting in near perfect accuracy as long as R<255.

Above this range, a small inaccuracy of a few pixels (at most) can be witnessed.

30pixels half circle : starts one pixel late, ends correctly

100pixels 3/4 circle : starts one pixel late, ends correctly

*Previous Versions :*Cyrille de Brebisson's Arc Toolbox V1.0 : HP48 S/G Binary (1215 Bytes)

with Source Code

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