mxwcore-legion/dep/g3dlite/source/LineSegment.cpp

/**
 @file LineSegment.cpp
  
 @maintainer Morgan McGuire, http://graphics.cs.williams.edu
 
 @created 2003-02-08
 @edited  2008-02-02
 */

#include "G3D/platform.h"
#include "G3D/LineSegment.h"
#include "G3D/Sphere.h"
#include "G3D/debug.h"

namespace G3D {


Vector3 LineSegment::closestPoint(const Vector3& p) const {

    // The vector from the end of the capsule to the point in question.
    Vector3 v(p - _point);

    // Projection of v onto the line segment scaled by 
    // the length of direction.
    float t = direction.dot(v);

    // Avoid some square roots.  Derivation:
    //    t/direction.length() <= direction.length()
    //      t <= direction.squaredLength()

    if ((t >= 0) && (t <= direction.squaredMagnitude())) {
    
        // The point falls within the segment.  Normalize direction,
        // divide t by the length of direction.
        return _point + direction * t / direction.squaredMagnitude();
    
    } else {

        // The point does not fall within the segment; see which end is closer.

        // Distance from 0, squared
        float d0Squared = v.squaredMagnitude();

        // Distance from 1, squared
        float d1Squared = (v - direction).squaredMagnitude();

        if (d0Squared < d1Squared) {

            // Point 0 is closer
            return _point;

        } else {

            // Point 1 is closer
            return _point + direction;
        
        }
    }

}

Vector3 LineSegment::point(int i) const {
    switch (i) {
    case 0:
        return _point;

    case 1:
        return _point + direction;

    default:
        debugAssertM(i == 0 || i == 1, "Argument to point must be 0 or 1");
        return _point;
    }
}


bool LineSegment::intersectsSolidSphere(const class Sphere& s) const {
    return distanceSquared(s.center) <= square(s.radius);
}


LineSegment::LineSegment(class BinaryInput& b) {
    deserialize(b);
}


void LineSegment::serialize(class BinaryOutput& b) const {
    _point.serialize(b);
    direction.serialize(b);
}


void LineSegment::deserialize(class BinaryInput& b) {
    _point.deserialize(b);
    direction.deserialize(b);
}


Vector3 LineSegment::randomPoint() const {
    return _point + uniformRandom(0, 1) * direction;
}


/////////////////////////////////////////////////////////////////////////////////////

LineSegment2D LineSegment2D::fromTwoPoints(const Vector2& p0, const Vector2& p1) {
    LineSegment2D s;
    s.m_origin      = p0;
    s.m_direction   = p1 - p0;
    s.m_length      = s.m_direction.length();
    return s;
}


Vector2 LineSegment2D::point(int i) const {
    debugAssert(i == 0 || i == 1);
    if (i == 0) {
        return m_origin;
    } else {
        return m_direction + m_origin;
    }
}


Vector2 LineSegment2D::closestPoint(const Vector2& Q) const {
    // Two constants that appear in the result
    const Vector2 k1(m_origin - Q);
    const Vector2& k2 = m_direction;
    
    if (fuzzyEq(m_length, 0)) {
        // This line segment has no length
        return m_origin;
    }

    // Time [0, 1] at which we hit the closest point travelling from p0 to p1.
    // Derivation can be obtained by minimizing the expression
    //     ||P0 + (P1 - P0)t - Q||.
    const float t = -k1.dot(k2) / (m_length * m_length);

    if (t < 0) {
        // Clipped to low end point
        return m_origin;
    } else if (t > 1) {
        // Clipped to high end point
        return m_origin + m_direction;
    } else {
        // Subsitute into the line equation to find 
        // the point on the segment.
        return m_origin + k2 * t;
    }
}


float LineSegment2D::distance(const Vector2& p) const {
    Vector2 closest = closestPoint(p);
    return (closest - p).length();
}


float LineSegment2D::length() const {
    return m_length;
}


Vector2 LineSegment2D::intersection(const LineSegment2D& other) const {

    if ((m_origin == other.m_origin) ||
        (m_origin == other.m_origin + other.m_direction)) {
        return m_origin;
    }

    if (m_origin + m_direction == other.m_origin) {
        return other.m_origin;
    }

    // Note: Now that we've checked the endpoints, all other parallel lines can now be assumed
    // to not intersect (within numerical precision)

    Vector2 dir1    = m_direction;
    Vector2 dir2    = other.m_direction;
    Vector2 origin1 = m_origin;
    Vector2 origin2 = other.m_origin;

    if (dir1.x == 0) {
        // Avoid an upcoming divide by zero
        dir1 = dir1.yx();
        dir2 = dir2.yx();
        origin1 = origin1.yx();
        origin2 = origin2.yx();
    }

    // t1 = ((other.m_origin.x - m_origin.x) + other.m_direction.x * t2) / m_direction.x
    //
    // ((other.m_origin.x - m_origin.x) + other.m_direction.x * t2) * m_direction.y / m_direction.x = 
    //        (other.m_origin.y - m_origin.y) + other.m_direction.y * t2
    //
    // m = m_direction.y / m_direction.x
    // d = other.m_origin - m_origin
    //
    // (d.x + other.m_direction.x * t2) * m = d.y + other.m_direction.y * t2
    //
    // d.x * m + other.m_direction.x * m * t2 = d.y + other.m_direction.y * t2
    //
    // d.x * m - d.y  = (other.m_direction.y - other.m_direction.x * m) * t2
    //
    // (d.x * m - d.y) / (other.m_direction.y - other.m_direction.x * m)  = t2
    //

    Vector2 d = origin2 - origin1;
    float m = dir1.y / dir1.x;

    float t2 = (d.x * m - d.y) / (dir2.y - dir2.x * m);
    if (! isFinite(t2)) {
        // Parallel lines: no intersection
        return Vector2::inf();
    }

    if ((t2 < 0.0f) || (t2 > 1.0f)) {
        // Intersection occurs past the end of the line segments
        return Vector2::inf();
    }

    float t1 = (d.x + dir2.x * t2) / dir1.x;
    if ((t1 < 0.0f) || (t1 > 1.0f)) {
        // Intersection occurs past the end of the line segments
        return Vector2::inf();
    }

    // Return the intersection point (computed from non-transposed 
    // variables even if we flipped above)
    return m_origin + m_direction * t1;
    
}

}