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ArcToMetafileCommandCreateCubicCurves Method

Calculates a set of cubic curves which are able to replace the arc.

Namespace: RAYLASE.Marker.VectorGraphicElement.MetafileCommand
Assembly: RAYLASE.Marker.VectorGraphicElement (in RAYLASE.Marker.VectorGraphicElement.dll) Version: 2.19.0
Syntax
C#
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public override List<CubicCurveToMetafileCommand> CreateCubicCurves()

Return Value

ListCubicCurveToMetafileCommand
The list of cubic curves representing the arc.
Remarks
An arc with center point C, start point S, sweep angle phi and end point E is to be replaced approximately by a cubic curve with the control points C0, C1, C2 and C3:
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^                                                                  
|                . . . . .                                        
|            .               .                                    
|          .                   .E = C4                              
|        .                   .   .                             
|       .                  .      ..                             
|      .                 .  \      . .                             
|      .               .     \     .   . C2                       
|      .           C .   phi  |    .                               
|      .               .     /     .   . C1                        
|      .                 .  /      . .                             
|       .                  .      ..                               
|        .                   .   .                              
|          .                   .                                   
|            .               .  S = C0                                 
|                . . . . .                                         
|                                                                  
+------------------------------------------------>
The control points have to be on the circle's tangents Ts and Te through the points S and E. This can be achieved by the formulas - C0 = S - C1 = S + l*Ts - C2 = E - l*Te - C3 = E with - Ts = Uz x CS (cross product between S-C and the unit vector in z direction) - Te = Uz x CE (cross product between E-C and the unit vector in z direction) - l = 4/3 * tan(phi/4) This is valid only for reasonable small angles phi, i. e. angles not larger than 90 degrees. Larger arcs are splitted therefore by deviding the sweep angle by 90 degrees.
See Also