MRTriPoint.h

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#pragma once
 
#include "MRVector3.h"
#include "MRSegmPoint.h"
 
namespace MR
{
 
template <typename T>
struct TriPoint
{
    T a; 
    T b; 
 
    static constexpr auto eps = SegmPoint<T>::eps;
 
    constexpr TriPoint() noexcept : a( 0 ), b( 0 ) { }
    explicit TriPoint( NoInit ) noexcept { }
    constexpr TriPoint( T a, T b ) noexcept : a( a ), b( b ) { }
    template <typename U>
    constexpr TriPoint( const TriPoint<U> & s ) : a( T( s.a ) ), b( T( s.b ) ) { }
 
    TriPoint( const Vector3<T> & p, const Vector3<T> & v0, const Vector3<T> & v1, const Vector3<T> & v2 ) : TriPoint( p - v0, v1 - v0, v2 - v0 ) { }
    TriPoint( const Vector3<T> & p, const Vector3<T> & v1, const Vector3<T> & v2 );
 
    template <typename U>
    U interpolate( const U & v0, const U & v1, const U & v2 ) const
        { return ( 1 - a - b ) * v0 + a * v1 + b * v2; }
 
    [[nodiscard]] TriPoint lnext() const { return { b, 1 - a - b }; }
 
    // requirements:
    // 1) inVertex() == onEdge() && toEdge()->inVertex()
    // 2) invariance to lnext() application
 
    constexpr int inVertex() const;
    constexpr int onEdge() const;
 
    [[nodiscard]] constexpr bool operator==( const TriPoint& rhs ) const = default;
};
 
 
template <typename T>
TriPoint<T>::TriPoint( const Vector3<T> & p, const Vector3<T> & v1, const Vector3<T> & v2 )
{
    const T v11 = dot( v1, v1 );
    const T v12 = dot( v1, v2 );
    const T v22 = dot( v2, v2 );
    const T det = v11 * v22 - v12 * v12;
    if ( det <= 0 )
    {
        // degenerate triangle
        a = b = 1 / T(3);
        return;
    }
    const T pv1 = dot( p, v1 );
    const T pv2 = dot( p, v2 );
    a = std::clamp( ( 1 / det ) * ( v22 * pv1 - v12 * pv2 ), T(0), T(1) );
    b = std::clamp( ( 1 / det ) * (-v12 * pv1 + v11 * pv2 ), T(0), T(1) - a );
}
 
template <typename T>
constexpr int TriPoint<T>::inVertex() const
{
    if ( a <= eps && b <= eps )
        return 0;
    if ( 1 - a - b <= eps )
    {
        if ( b <= eps )
            return 1;
        if ( a <= eps )
            return 2;
    }
    return -1;
}
 
template <typename T>
constexpr int TriPoint<T>::onEdge() const
{
    if ( 1 - a - b <= eps )
        return 0;
    if ( a <= eps )
        return 1;
    if ( b <= eps )
        return 2;
    return -1;
}
 
 
} // namespace MR