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Added closest point on a line to a line #81

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68 changes: 65 additions & 3 deletions olcUTIL_Geometry2D.h
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
/*
/*
OneLoneCoder - Geometry 2D v2.0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A collection of 2D Geometric primitives and functions to work with
Expand Down Expand Up @@ -899,8 +899,70 @@ namespace olc::utils::geom2d
template<typename T1, typename T2>
inline olc::v_2d<T1> closest(const line<T1>& l1, const line<T2>& l2)
{
// TODO:
return {};
auto dirA = l1.end - l1.start;
auto dirB = l2.end - l2.start;

auto dotA = dirA.dot(dirA);
auto dotB = dirB.dot(dirB);
auto dotAB = dirA.dot(dirB);

auto diff = l2.start - l1.start;
// denominator for t & s parameters
auto denom = dotA * dotB - dotAB * dotAB;
T1 t, s;

if (denom > 1e-6f) {
// lines are not parallel (or almost parallel)
auto invDenom = 1.0f / denom;

// unnormalized parameters
auto t_nom = dotB * diff.dot(dirA) - dotAB * diff.dot(dirB);
auto s_nom = dotA * diff.dot(dirB) - dotAB * diff.dot(dirA);

t = t_nom * invDenom;
s = s_nom * invDenom;
}
else {
// Parallel or nearly parallel → project b.start onto A and clamp
t = diff.dot(dirA) / dotA;
s = 0;
}

if (t < 0) t = 0;
if (t > 1) t = 1;

// Candidate point on A
auto closestOnA = l1.start + (dirA * t);

// Find closest point on B to this candidate (and clamp to B)
auto t_B = (closestOnA - l2.start).dot(dirB) / dotB;
auto pointOnB = l2.start + (dirB * t_B);

// Clamp to segment B
if (dotB > 1e-8f) {
auto s_clamped = (pointOnB - l2.start).dot(dirB) / dotB;
if (s_clamped < 0) s_clamped = 0;
if (s_clamped > 1) s_clamped = 1;
pointOnB = l2.start + (dirB * s_clamped);
}
else {
// degenerate B - just a point
pointOnB = l2.start;
}

// Final closest point on A is the projection of pointOnB back onto A
auto t_A = (pointOnB - l1.start).dot(dirA) / dotA;
closestOnA = l1.start + (dirA * t_A);

// Last clamp (handles degenerate cases and numerical issues)
T1 t_final = 0;
if (dotA > 1e-8f) {
t_final = (closestOnA - l1.start).dot(dirA) / dotA;
if (t_final < 0) t_final = 0;
if (t_final > 1) t_final = 1;
}

return l1.start + (dirA * t_final);
}

// closest(r,l)
Expand Down