2.1.1316 Part 1 Section 20.1.10.9, ST_BevelPresetType (Bevel Presets)

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a.   The standard contains a table with examples of the enumeration values, but the examples do not describe how the bevels are defined.

Office defines each bevel as 2D curves in a square unit space ({0, 0} to {1, 1}). Unlike a real-world bevel which cuts away from a surface, these conceptually extend a flat face perpendicular to that face.

The schema also has bevel width and bevel height attributes. The point (0,0) in this "bevel space" is at the outer edge of the face, the x-coordinate moves away from the face (along the "bevel height"), while the y-coordinate moves inwards towards the interior of the face (along the "bevel width"). The two dimensions in the bevel space are also treated differently in that Office stretches the x-axis to fully fill the bevel height.

[Example:

Bevel type "cross" ends with x == 0.6, but the geometry created is as tall as with bevel type "angle" which ends at x == 1.0. But for the y-axis Office scales the bevel from {0..1} to {0..bevelWidth}, so that a bevel ending with a point at y < 1 will not move as deeply towards the interior of the shape.

end example]

Below is pseudocode to assemble geometry for each of the bevel types.

 angle:
    BeginFigure( { 0, 0 } );
    LineTo( { 1, 1 } );
  
 artDeco:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.000000, 0.184095 }, { 0.149238, 0.333333 }, { 0.333333, 0.333333 } );
    BezierTo( { 0.333333, 0.701523 }, { 0.631810, 1.000000 }, { 1.000000, 1.000000 } );
  
 circle:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.00000, 0.55627 }, { 0.44373, 1.00000 }, { 1.00000, 1.00000 } );
  
 convex:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.0000000, 0.070820 }, { 0.0297458, 0.100000 }, { 0.1014160, 0.100000 } );
    BezierTo( { 0.5014160, 0.100000 }, { 0.9000000, 0.700000 }, { 0.9014160, 0.899999 } );
    BezierTo( { 0.9000000, 0.971670 }, { 0.9334300, 1.000000 }, { 1.0000000, 1.000000 } );
  
 coolSlant:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.000000, 0.138122 }, { 0.000000, 0.200000 }, { 0.271356, 0.775535 } );
    BezierTo( { 0.377654, 1.000000 }, { 0.519455, 1.000000 }, { 0.583589, 1.000000 } );
  
 cross:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.00000, 0.05563 }, { 0.04437, 0.10000 }, { 0.10000, 0.10000 } );
    LineTo( { 0.40000, 0.10000 } );
    BezierTo( { 0.45563, 0.10000 }, { 0.50000, 0.14437 }, { 0.50000, 0.20000 } );
    LineTo( { 0.50000, 0.90000 } );
    BezierTo( { 0.50000, 0.95563 }, { 0.54437, 1.00000 }, { 0.60000, 1.00000 } );
  
  
 divot:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.000000, 0.236604 }, { 0.119276, 0.607024 }, { 0.263046, 0.760235 } );
    BezierTo( { 0.361098, 0.864726 }, { 0.457934, 0.909567 }, { 0.537806, 0.925082 } );
    BezierTo( { 0.559245, 0.929246 }, { 0.567625, 0.897930 }, { 0.542066, 0.845567 } );
    BezierTo( { 0.484073, 0.726757 }, { 0.477103, 0.393693 }, { 0.551651, 0.393693 } );
    LineTo( { 0.899894, 0.393693 } );
    BezierTo( { 0.991480, 0.393693 }, { 0.958466, 0.746659 }, { 0.907348, 0.779629 } );
    LineTo( { 0.879394, 0.797658 } );
    BezierTo( { 0.845545, 0.819489 }, { 0.848775, 0.954172 }, { 0.874334, 0.971627 } );
    QuadraticBezierTo( { 0.915883, 1.000000 }, { 1.000000, 1.000000 } );
  
 hardEdge:
    BeginFigure( { 0, 0 } );
    QuadraticBezierTo( { 0.000000, 0.092437 }, { 0.042353, 0.305322 } );
    LineTo( { 0.170124, 0.947558 } );
    BezierTo( { 0.177203, 0.983142 }, { 0.200000, 1.000000 }, { 0.268235, 0.998599 } );
    LineTo( { 0.614118, 0.998599 } );
    BezierTo( { 0.647059, 0.998599 }, { 0.656471, 0.987395 }, { 0.663529, 0.969188 } );
    BezierTo( { 0.687006, 0.908633 }, { 0.802353, 0.822129 }, { 1.000000, 0.822129 } );
  
 relaxedInset:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.000000, 0.367 }, { 0.124605, 0.820 }, { 0.507899, 1.000 } );
    BezierTo( { 0.724115, 0.737 }, { 0.790455, 0.640 }, { 1.000000, 0.640 } );
  
 riblet:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.000000, 0.238519 }, { 0.132047, 0.500741 }, { 0.357567, 0.731852 } );
    BezierTo( { 0.513167, 0.891311 }, { 0.563798, 0.912593 }, { 0.735905, 0.912593 } );
    LineTo( { 0.873887, 0.912593 } );
    BezierTo( { 0.956973, 0.912593 }, { 0.878338, 1.000000 }, { 1.000000, 1.000000 } );
  
 slope:
    BeginFigure( { 0, 0 } );
    QuadraticBezierTo( { 0.00000, 0.12500 }, { 0.02500, 0.25000 } );
    LineTo( { 0.12500, 0.75000 } );
    BezierTo( { 0.17500, 1.00000 }, { 0.25000, 1.00000 }, { 0.37500, 1.00000 } );
    LineTo( { 0.50000, 1.00000 } );
    BezierTo( { 0.62500, 1.00000 }, { 0.70000, 1.00000 }, { 0.75000, 0.75000 } );
    LineTo( { 0.87500, 0.12500 } );
    BezierTo( { 0.90000, 0.01000 }, { 0.98000, 0.01000 }, { 1.00000, 0.01000 } );
  
 softRound:
    BeginFigure( { 0, 0 } );
    BezierTo( { 0.0000000, 0.47750 }, { 0.0968736, 1.00000 }, { 0.1563010, 1.00000 } );
    BezierTo( { 0.2641790, 1.00000 }, { 0.3769190, 0.33333 }, { 1.0000000, 0.33333 } );