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Bezier: add the function to get point at t

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Not of huge practical use on its own, but other maths will
need this.
This commit is contained in:
John Beard 2024-09-27 06:56:01 +01:00
parent 98830577eb
commit 4e2162fc97
1 changed files with 25 additions and 3 deletions

28
libs/kimath/include/bezier_curves.h
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@ -96,10 +96,32 @@ class BEZIER
public:
BEZIER() = default;
BEZIER( const VECTOR2<NumericType>& aStart, const VECTOR2<NumericType>& aC1,
const VECTOR2<NumericType>& aC2, const VECTOR2<NumericType>& aEnd ) :
constexpr BEZIER( const VECTOR2<NumericType>& aStart, const VECTOR2<NumericType>& aC1,
const VECTOR2<NumericType>& aC2, const VECTOR2<NumericType>& aEnd ) :
Start( aStart ), C1( aC1 ), C2( aC2 ), End( aEnd )
{}
{
}
/**
* Evaluate the Bezier curve at a given t value
*
* aT doesn't have to be in the range [0, 1], but if it's not, the
* point will not be on the curve.
*
* @param aT the t value to evaluate the curve at (0 = start, 1 = end)
* @return the point on the curve at t (0 <= t <= 1)
*/
constexpr VECTOR2<NumericType> PointAt( double aT ) const
{
const double t2 = aT * aT;
const double t3 = t2 * aT;
const double t_m1 = 1.0 - aT;
const double t_m1_2 = t_m1 * t_m1;
const double t_m1_3 = t_m1_2 * t_m1;
return ( t_m1_3 * Start ) + ( 3.0 * aT * t_m1_2 * C1 ) + ( 3.0 * t2 * t_m1 * C2 )
+ ( t3 * End );
}
VECTOR2<NumericType> Start;
VECTOR2<NumericType> C1;