////  AABox.cpp//  libraries/octree/src////  Created by Brad Hefta-Gaub on 04/11/13.//  Copyright 2013 High Fidelity, Inc.////  Distributed under the Apache License, Version 2.0.//  See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html// #include "AABox.h" #include "AACube.h"#include "Transform.h"#include "Extents.h"#include "GeometryUtil.h"#include "NumericalConstants.h" const glm::vec3 AABox::INFINITY_VECTOR(std::numeric_limits<float>::infinity()); AABox::AABox(const AACube& other) :    _corner(other.getCorner()), _scale(other.getScale(), other.getScale(), other.getScale()) {} AABox::AABox(const Extents& other) :    _corner(other.minimum),    _scale(other.maximum - other.minimum) {} AABox::AABox(const glm::vec3& corner, float size) :    _corner(corner), _scale(size, size, size) {}; AABox::AABox(const glm::vec3& corner, const glm::vec3& dimensions) :    _corner(corner), _scale(dimensions) {}; AABox::AABox() : _corner(INFINITY_VECTOR), _scale(0.0f) {}; glm::vec3 AABox::calcCenter() const {    glm::vec3 center(_corner);    center += (_scale * 0.5f);    return center;} glm::vec3 AABox::getVertex(BoxVertex vertex) const {    switch (vertex) {        case BOTTOM_LEFT_NEAR:            return _corner + glm::vec3(_scale.x, 0, 0);        case BOTTOM_RIGHT_NEAR:            return _corner;        case TOP_RIGHT_NEAR:            return _corner + glm::vec3(0, _scale.y, 0);        case TOP_LEFT_NEAR:            return _corner + glm::vec3(_scale.x, _scale.y, 0);        case BOTTOM_LEFT_FAR:            return _corner + glm::vec3(_scale.x, 0, _scale.z);        case BOTTOM_RIGHT_FAR:            return _corner + glm::vec3(0, 0, _scale.z);        case TOP_RIGHT_FAR:            return _corner + glm::vec3(0, _scale.y, _scale.z);        default: //quiet windows warnings        case TOP_LEFT_FAR:            return _corner + _scale;    }} void AABox::setBox(const glm::vec3& corner, float scale) {    _corner = corner;    _scale = glm::vec3(scale, scale, scale);} void AABox::setBox(const glm::vec3& corner, const glm::vec3& scale) {    _corner = corner;    _scale = scale;} glm::vec3 AABox::getFarthestVertex(const glm::vec3& normal) const {    glm::vec3 result = _corner;    // This is a branchless version of:    //if (normal.x > 0.0f) {    //    result.x += _scale.x;    //}    //if (normal.y > 0.0f) {    //    result.y += _scale.y;    //}    //if (normal.z > 0.0f) {    //    result.z += _scale.z;    //}    float blend = (float)(normal.x > 0.0f);    result.x += blend * _scale.x + (1.0f - blend) * 0.0f;    blend = (float)(normal.y > 0.0f);    result.y += blend * _scale.y + (1.0f - blend) * 0.0f;    blend = (float)(normal.z > 0.0f);    result.z += blend * _scale.z + (1.0f - blend) * 0.0f;    return result;} glm::vec3 AABox::getNearestVertex(const glm::vec3& normal) const {    glm::vec3 result = _corner;    // This is a branchless version of:    //if (normal.x < 0.0f) {    //    result.x += _scale.x;    //}    //if (normal.y < 0.0f) {    //    result.y += _scale.y;    //}    //if (normal.z < 0.0f) {    //    result.z += _scale.z;    //}    float blend = (float)(normal.x < 0.0f);    result.x += blend * _scale.x + (1.0f - blend) * 0.0f;    blend = (float)(normal.y < 0.0f);    result.y += blend * _scale.y + (1.0f - blend) * 0.0f;    blend = (float)(normal.z < 0.0f);    result.z += blend * _scale.z + (1.0f - blend) * 0.0f;    return result;} bool AABox::contains(const Triangle& triangle) const {    return contains(triangle.v0) && contains(triangle.v1) && contains(triangle.v2);} bool AABox::contains(const glm::vec3& point) const {    return aaBoxContains(point, _corner, _scale);} bool AABox::contains(const AABox& otherBox) const {    for (int v = BOTTOM_LEFT_NEAR; v < TOP_LEFT_FAR; v++) {        glm::vec3 vertex = otherBox.getVertex((BoxVertex)v);        if (!contains(vertex)) {            return false;        }    }    return true;} bool AABox::touches(const AABox& otherBox) const {    glm::vec3 relativeCenter = _corner - otherBox._corner + ((_scale - otherBox._scale) * 0.5f);     glm::vec3 totalHalfScale = (_scale + otherBox._scale) * 0.5f;     return fabsf(relativeCenter.x) <= totalHalfScale.x &&        fabsf(relativeCenter.y) <= totalHalfScale.y &&        fabsf(relativeCenter.z) <= totalHalfScale.z;} bool AABox::contains(const AACube& otherCube) const {    for (int v = BOTTOM_LEFT_NEAR; v < TOP_LEFT_FAR; v++) {        glm::vec3 vertex = otherCube.getVertex((BoxVertex)v);        if (!contains(vertex)) {            return false;        }    }    return true;} bool AABox::touches(const AACube& otherCube) const {    glm::vec3 relativeCenter = _corner - otherCube.getCorner() + ((_scale - otherCube.getDimensions()) * 0.5f);     glm::vec3 totalHalfScale = (_scale + otherCube.getDimensions()) * 0.5f;     return fabsf(relativeCenter.x) <= totalHalfScale.x &&        fabsf(relativeCenter.y) <= totalHalfScale.y &&        fabsf(relativeCenter.z) <= totalHalfScale.z;} // determines whether a value is within the expanded extentsstatic bool isWithinExpanded(float value, float corner, float size, float expansion) {    return value >= corner - expansion && value <= corner + size + expansion;} bool AABox::expandedContains(const glm::vec3& point, float expansion) const {    return isWithinExpanded(point.x, _corner.x, _scale.x, expansion) &&        isWithinExpanded(point.y, _corner.y, _scale.y, expansion) &&        isWithinExpanded(point.z, _corner.z, _scale.z, expansion);} bool AABox::expandedIntersectsSegment(const glm::vec3& start, const glm::vec3& end, float expansion) const {    // handle the trivial cases where the expanded box contains the start or end    if (expandedContains(start, expansion) || expandedContains(end, expansion)) {        return true;    }    // check each axis    glm::vec3 expandedCorner = _corner - glm::vec3(expansion, expansion, expansion);    glm::vec3 expandedSize = _scale + glm::vec3(expansion, expansion, expansion) * 2.0f;    glm::vec3 direction = end - start;    float axisDistance;    return (findIntersection(start.x, direction.x, expandedCorner.x, expandedSize.x, axisDistance) &&                axisDistance >= 0.0f && axisDistance <= 1.0f &&                isWithin(start.y + axisDistance*direction.y, expandedCorner.y, expandedSize.y) &&                isWithin(start.z + axisDistance*direction.z, expandedCorner.z, expandedSize.z)) ||           (findIntersection(start.y, direction.y, expandedCorner.y, expandedSize.y, axisDistance) &&                axisDistance >= 0.0f && axisDistance <= 1.0f &&                isWithin(start.x + axisDistance*direction.x, expandedCorner.x, expandedSize.x) &&                isWithin(start.z + axisDistance*direction.z, expandedCorner.z, expandedSize.z)) ||           (findIntersection(start.z, direction.z, expandedCorner.z, expandedSize.z, axisDistance) &&                axisDistance >= 0.0f && axisDistance <= 1.0f &&                isWithin(start.y + axisDistance*direction.y, expandedCorner.y, expandedSize.y) &&                isWithin(start.x + axisDistance*direction.x, expandedCorner.x, expandedSize.x));} bool AABox::findRayIntersection(const glm::vec3& origin, const glm::vec3& direction, const glm::vec3& invDirection,                                float& distance, BoxFace& face, glm::vec3& surfaceNormal) const {    return findRayAABoxIntersection(origin, direction, invDirection, _corner, _scale, distance, face, surfaceNormal);} bool AABox::findParabolaIntersection(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration,                                     float& parabolicDistance, BoxFace& face, glm::vec3& surfaceNormal) const {    return findParabolaAABoxIntersection(origin, velocity, acceleration, _corner, _scale, parabolicDistance, face, surfaceNormal);} bool AABox::rayHitsBoundingSphere(const glm::vec3& origin, const glm::vec3& direction) const {    glm::vec3 localCenter = calcCenter() - origin;    float distance = glm::dot(localCenter, direction);    const float ONE_OVER_TWO_SQUARED = 0.25f;    float radiusSquared = ONE_OVER_TWO_SQUARED * glm::length2(_scale);    return (glm::length2(localCenter) < radiusSquared            || (glm::abs(distance) > 0.0f && glm::distance2(distance * direction, localCenter) < radiusSquared));} bool AABox::parabolaPlaneIntersectsBoundingSphere(const glm::vec3& origin, const glm::vec3& velocity, const glm::vec3& acceleration, const glm::vec3& normal) const {    glm::vec3 localCenter = calcCenter() - origin;    const float ONE_OVER_TWO_SQUARED = 0.25f;    float radiusSquared = ONE_OVER_TWO_SQUARED * glm::length2(_scale);     // origin is inside the sphere    if (glm::length2(localCenter) < radiusSquared) {        return true;    }     if (glm::length2(acceleration) < EPSILON) {        // Handle the degenerate case where acceleration == (0, 0, 0)        return rayHitsBoundingSphere(origin, glm::normalize(velocity));    } else {        // Project vector from plane to sphere center onto the normal        float distance = glm::dot(localCenter, normal);        if (distance * distance < radiusSquared) {            return true;        }    }    return false;} bool AABox::touchesSphere(const glm::vec3& center, float radius) const {    // Avro's algorithm from this paper: http://www.mrtc.mdh.se/projects/3Dgraphics/paperF.pdf    glm::vec3 e = glm::max(_corner - center, Vectors::ZERO) + glm::max(center - _corner - _scale, Vectors::ZERO);    return glm::length2(e) <= radius * radius;} bool AABox::findSpherePenetration(const glm::vec3& center, float radius, glm::vec3& penetration) const {    glm::vec4 center4 = glm::vec4(center, 1.0f);     float minPenetrationLength = FLT_MAX;    for (int i = 0; i < FACE_COUNT; i++) {        glm::vec4 facePlane = getPlane((BoxFace)i);        glm::vec3 vector = getClosestPointOnFace(center, (BoxFace)i) - center;        if (glm::dot(center4, getPlane((BoxFace)i)) >= 0.0f) {            // outside this face, so use vector to closest point to determine penetration            return ::findSpherePenetration(vector, glm::vec3(-facePlane), radius, penetration);        }        float vectorLength = glm::length(vector);        if (vectorLength < minPenetrationLength) {            // remember the smallest penetration vector; if we're inside all faces, we'll use that            penetration = (vectorLength < EPSILON) ? glm::vec3(-facePlane) * radius :                vector * ((vectorLength + radius) / -vectorLength);            minPenetrationLength = vectorLength;        }    }     return true;} bool AABox::findCapsulePenetration(const glm::vec3& start, const glm::vec3& end, float radius, glm::vec3& penetration) const {    glm::vec4 start4 = glm::vec4(start, 1.0f);    glm::vec4 end4 = glm::vec4(end, 1.0f);    glm::vec4 startToEnd = glm::vec4(end - start, 0.0f);     float minPenetrationLength = FLT_MAX;    for (int i = 0; i < FACE_COUNT; i++) {        // find the vector from the segment to the closest point on the face (starting from deeper end)        glm::vec4 facePlane = getPlane((BoxFace)i);        glm::vec3 closest = (glm::dot(start4, facePlane) <= glm::dot(end4, facePlane)) ?            getClosestPointOnFace(start4, startToEnd, (BoxFace)i) : getClosestPointOnFace(end4, -startToEnd, (BoxFace)i);        glm::vec3 vector = -computeVectorFromPointToSegment(closest, start, end);        if (glm::dot(vector, glm::vec3(facePlane)) < 0.0f) {            // outside this face, so use vector to closest point to determine penetration            return ::findSpherePenetration(vector, glm::vec3(-facePlane), radius, penetration);        }        float vectorLength = glm::length(vector);        if (vectorLength < minPenetrationLength) {            // remember the smallest penetration vector; if we're inside all faces, we'll use that            penetration = (vectorLength < EPSILON) ? glm::vec3(-facePlane) * radius :                vector * ((vectorLength + radius) / -vectorLength);            minPenetrationLength = vectorLength;        }    }     return true;} glm::vec3 AABox::getClosestPointOnFace(const glm::vec3& point, BoxFace face) const {    switch (face) {        case MIN_X_FACE:            return glm::clamp(point, glm::vec3(_corner.x, _corner.y, _corner.z),                glm::vec3(_corner.x, _corner.y + _scale.y, _corner.z + _scale.z));         case MAX_X_FACE:            return glm::clamp(point, glm::vec3(_corner.x + _scale.x, _corner.y, _corner.z),                glm::vec3(_corner.x + _scale.x, _corner.y + _scale.y, _corner.z + _scale.z));         case MIN_Y_FACE:            return glm::clamp(point, glm::vec3(_corner.x, _corner.y, _corner.z),                glm::vec3(_corner.x + _scale.x, _corner.y, _corner.z + _scale.z));         case MAX_Y_FACE:            return glm::clamp(point, glm::vec3(_corner.x, _corner.y + _scale.y, _corner.z),                glm::vec3(_corner.x + _scale.x, _corner.y + _scale.y, _corner.z + _scale.z));         case MIN_Z_FACE:            return glm::clamp(point, glm::vec3(_corner.x, _corner.y, _corner.z),                glm::vec3(_corner.x + _scale.x, _corner.y + _scale.y, _corner.z));         default: //quiet windows warnings        case MAX_Z_FACE:            return glm::clamp(point, glm::vec3(_corner.x, _corner.y, _corner.z + _scale.z),                glm::vec3(_corner.x + _scale.x, _corner.y + _scale.y, _corner.z + _scale.z));    }} glm::vec3 AABox::getClosestPointOnFace(const glm::vec4& origin, const glm::vec4& direction, BoxFace face) const {    // check against the four planes that border the face    BoxFace oppositeFace = getOppositeFace(face);    bool anyOutside = false;    for (int i = 0; i < FACE_COUNT; i++) {        if (i == face || i == oppositeFace) {            continue;        }        glm::vec4 iPlane = getPlane((BoxFace)i);        float originDistance = glm::dot(origin, iPlane);        if (originDistance < 0.0f) {            continue; // inside the border        }        anyOutside = true;        float divisor = glm::dot(direction, iPlane);        if (fabsf(divisor) < EPSILON) {            continue; // segment is parallel to plane        }        // find intersection and see if it lies within face bounds        float directionalDistance = -originDistance / divisor;        glm::vec4 intersection = origin + direction * directionalDistance;        BoxFace iOppositeFace = getOppositeFace((BoxFace)i);        for (int j = 0; j < FACE_COUNT; j++) {            if (j == face || j == oppositeFace || j == i || j == iOppositeFace) {                continue;            }            if (glm::dot(intersection, getPlane((BoxFace)j)) > 0.0f) {                goto outerContinue; // intersection is out of bounds            }        }        return getClosestPointOnFace(glm::vec3(intersection), face);         outerContinue: ;    }     // if we were outside any of the sides, we must check against the diagonals    if (anyOutside) {        int faceAxis = face / 2;        int secondAxis = (faceAxis + 1) % 3;        int thirdAxis = (faceAxis + 2) % 3;         glm::vec4 secondAxisMinPlane = getPlane((BoxFace)(secondAxis * 2));        glm::vec4 secondAxisMaxPlane = getPlane((BoxFace)(secondAxis * 2 + 1));        glm::vec4 thirdAxisMaxPlane = getPlane((BoxFace)(thirdAxis * 2 + 1));         glm::vec4 offset = glm::vec4(0.0f, 0.0f, 0.0f,            glm::dot(glm::vec3(secondAxisMaxPlane + thirdAxisMaxPlane), _scale) * 0.5f);        glm::vec4 diagonals[] = { secondAxisMinPlane + thirdAxisMaxPlane + offset,            secondAxisMaxPlane + thirdAxisMaxPlane + offset };         float minDistance = FLT_MAX;        for (size_t i = 0; i < sizeof(diagonals) / sizeof(diagonals[0]); i++) {            float divisor = glm::dot(direction, diagonals[i]);            if (fabsf(divisor) < EPSILON) {                continue; // segment is parallel to diagonal plane            }            minDistance = glm::min(-glm::dot(origin, diagonals[i]) / divisor, minDistance);        }        if (minDistance != FLT_MAX) {            return getClosestPointOnFace(glm::vec3(origin + direction * minDistance), face);        }    }     // last resort or all inside: clamp origin to face    return getClosestPointOnFace(glm::vec3(origin), face);} bool AABox::touchesAAEllipsoid(const glm::vec3& center, const glm::vec3& radials) const {    // handle case where ellipsoid's alix-aligned box doesn't touch this AABox    if (_corner.x - radials.x > center.x ||        _corner.y - radials.y > center.y ||        _corner.z - radials.z > center.z ||        _corner.x + _scale.x + radials.x < center.x ||        _corner.y + _scale.y + radials.y < center.y ||        _corner.z + _scale.z + radials.z < center.z) {        return false;    }     // handle case where ellipsoid is entirely inside this AABox    if (contains(center)) {        return true;    }     for (int i = 0; i < FACE_COUNT; i++) {        glm::vec3 closest = getClosestPointOnFace(center, (BoxFace)i) - center;        float x = closest.x;        float y = closest.y;        float z = closest.z;        float a = radials.x;        float b = radials.y;        float c = radials.z;        if (x*x/(a*a) + y*y/(b*b) + z*z/(c*c) < 1.0f) {            return true;        }    }    return false;}  glm::vec4 AABox::getPlane(BoxFace face) const {    switch (face) {        case MIN_X_FACE: return glm::vec4(-1.0f, 0.0f, 0.0f, _corner.x);        case MAX_X_FACE: return glm::vec4(1.0f, 0.0f, 0.0f, -_corner.x - _scale.x);        case MIN_Y_FACE: return glm::vec4(0.0f, -1.0f, 0.0f, _corner.y);        case MAX_Y_FACE: return glm::vec4(0.0f, 1.0f, 0.0f, -_corner.y - _scale.y);        case MIN_Z_FACE: return glm::vec4(0.0f, 0.0f, -1.0f, _corner.z);        default: //quiet windows warnings        case MAX_Z_FACE: return glm::vec4(0.0f, 0.0f, 1.0f, -_corner.z - _scale.z);    }} BoxFace AABox::getOppositeFace(BoxFace face) {    switch (face) {        case MIN_X_FACE: return MAX_X_FACE;        case MAX_X_FACE: return MIN_X_FACE;        case MIN_Y_FACE: return MAX_Y_FACE;        case MAX_Y_FACE: return MIN_Y_FACE;        case MIN_Z_FACE: return MAX_Z_FACE;        default: //quiet windows warnings        case MAX_Z_FACE: return MIN_Z_FACE;    }} AABox AABox::clamp(const glm::vec3& min, const glm::vec3& max) const {    glm::vec3 clampedCorner = glm::clamp(_corner, min, max);    glm::vec3 clampedTopFarLeft = glm::clamp(calcTopFarLeft(), min, max);    glm::vec3 clampedScale = clampedTopFarLeft - clampedCorner;     return AABox(clampedCorner, clampedScale);} AABox AABox::clamp(float min, float max) const {    glm::vec3 clampedCorner = glm::clamp(_corner, min, max);    glm::vec3 clampedTopFarLeft = glm::clamp(calcTopFarLeft(), min, max);    glm::vec3 clampedScale = clampedTopFarLeft - clampedCorner;     return AABox(clampedCorner, clampedScale);} void AABox::embiggen(float scale) {    _corner += scale * (-0.5f * _scale);    _scale *= scale;} void AABox::embiggen(const glm::vec3& scale) {    _corner += scale * (-0.5f * _scale);    _scale *= scale;} void AABox::setScaleStayCentered(const glm::vec3& scale) {    _corner -= 0.5f * (scale - _scale);    _scale = scale;} void AABox::scale(float scale) {    _corner *= scale;    _scale *= scale;} void AABox::scale(const glm::vec3& scale) {    _corner *= scale;    _scale *= scale;} void AABox::rotate(const glm::quat& rotation) {    auto minimum = _corner;    auto maximum = _corner + _scale; 

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