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Add principle of checking the spline to comment
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The way of checking the spline is flat or not is to calculate the
distance from a control point to the line connected by the point A and
point D, which is based on the Convex Hull Property of Bézier Curves
that Bézier Curve lies within the convex hull of its control points.
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weihsinyeh committed Aug 19, 2024
1 parent c782f22 commit ee7d0f5
Showing 1 changed file with 4 additions and 1 deletion.
5 changes: 4 additions & 1 deletion src/spline.c
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Expand Up @@ -57,7 +57,10 @@ static void _de_casteljau(twin_spline_t *spline,

/*
* Return an upper bound on the distance (squared) that could result from
* approximating a spline with a line segment connecting the two endpoints.
* approximating a spline with a line segment connecting the two endpoints,
* which is based on the Convex Hull Property of Bézier Curves: The Bézier Curve
* lies completely in the convex hull of the given control points. Therefore, we
* can use control points B and C to approximate the actual spline.
*/
static twin_dfixed_t _twin_spline_distance_squared(twin_spline_t *spline)
{
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