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chore: update intersect and improve documentation

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Signed-off-by: Michael Pollind <mpollind@gmail.com>
This commit is contained in:
Michael Pollind
2021-10-09 21:10:08 -07:00
parent 7b1dd01d1d
commit afa8bb9226
4 changed files with 485 additions and 299 deletions
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Code/Framework/AzCore/AzCore/Math/IntersectSegment.cpp
+18 -15
View File
@@ -157,7 +157,7 @@ Intersect::IntersectSegmentTriangle(
// TestSegmentAABBOrigin
// [10/21/2009]
//=========================================================================
int
bool
AZ::Intersect::TestSegmentAABBOrigin(const Vector3& midPoint, const Vector3& halfVector, const Vector3& aabbExtends)
{
const Vector3 EPSILON(0.001f); // \todo this is slow load move to a const
@@ -168,7 +168,7 @@ AZ::Intersect::TestSegmentAABBOrigin(const Vector3& midPoint, const Vector3& hal
// Try world coordinate axes as separating axes
if (!absMidpoint.IsLessEqualThan(absHalfMidpoint))
{
return 0;
return false;
}
// Add in an epsilon term to counteract arithmetic errors when segment is
@@ -188,11 +188,11 @@ AZ::Intersect::TestSegmentAABBOrigin(const Vector3& midPoint, const Vector3& hal
Vector3 ead(ey * adz + ez * ady, ex * adz + ez * adx, ex * ady + ey * adx);
if (!absMDCross.IsLessEqualThan(ead))
{
return 0;
return false;
}
// No separating axis found; segment must be overlapping AABB
return 1;
return true;
}
@@ -200,7 +200,7 @@ AZ::Intersect::TestSegmentAABBOrigin(const Vector3& midPoint, const Vector3& hal
// IntersectRayAABB
// [10/21/2009]
//=========================================================================
int
RayAABBIsectTypes
AZ::Intersect::IntersectRayAABB(
const Vector3& rayStart, const Vector3& dir, const Vector3& dirRCP, const Aabb& aabb,
float& tStart, float& tEnd, Vector3& startNormal /*, Vector3& inter*/)
@@ -352,11 +352,14 @@ AZ::Intersect::IntersectRayAABB(
return ISECT_RAY_AABB_ISECT;
}
//=========================================================================
// IntersectRayAABB2
// [2/18/2011]
//=========================================================================
int
RayAABBIsectTypes
AZ::Intersect::IntersectRayAABB2(const Vector3& rayStart, const Vector3& dirRCP, const Aabb& aabb, float& start, float& end)
{
float tmin, tmax, tymin, tymax, tzmin, tzmax;
@@ -1166,7 +1169,7 @@ int AZ::Intersect::IntersectRayObb(const Vector3& rayOrigin, const Vector3& rayD
// IntersectSegmentCylinder
// [10/21/2009]
//=========================================================================
int
CylinderIsectTypes
AZ::Intersect::IntersectSegmentCylinder(
const Vector3& sa, const Vector3& dir, const Vector3& p, const Vector3& q, const float r, float& t)
{
@@ -1225,7 +1228,7 @@ AZ::Intersect::IntersectSegmentCylinder(
return RR_ISECT_RAY_CYL_NONE; // No real roots; no intersection
}
t = (-b - Sqrt(discr)) / a;
int result = RR_ISECT_RAY_CYL_PQ; // default along the PQ segment
CylinderIsectTypes result = RR_ISECT_RAY_CYL_PQ; // default along the PQ segment
if (md + t * nd < 0.0f)
{
@@ -1294,7 +1297,7 @@ AZ::Intersect::IntersectSegmentCylinder(
// IntersectSegmentCapsule
// [10/21/2009]
//=========================================================================
int
CapsuleIsectTypes
AZ::Intersect::IntersectSegmentCapsule(const Vector3& sa, const Vector3& dir, const Vector3& p, const Vector3& q, const float r, float& t)
{
int result = IntersectSegmentCylinder(sa, dir, p, q, r, t);
@@ -1361,7 +1364,7 @@ AZ::Intersect::IntersectSegmentCapsule(const Vector3& sa, const Vector3& dir, co
// IntersectSegmentPolyhedron
// [10/21/2009]
//=========================================================================
int
bool
AZ::Intersect::IntersectSegmentPolyhedron(
const Vector3& sa, const Vector3& sBA, const Plane p[], int numPlanes,
float& tfirst, float& tlast, int& iFirstPlane, int& iLastPlane)
@@ -1388,7 +1391,7 @@ AZ::Intersect::IntersectSegmentPolyhedron(
// If so, return "no intersection" if segment lies outside plane
if (dist < 0.0f)
{
return 0;
return false;
}
}
else
@@ -1417,7 +1420,7 @@ AZ::Intersect::IntersectSegmentPolyhedron(
// Exit with "no intersection" if intersection becomes empty
if (tfirst > tlast)
{
return 0;
return false;
}
}
}
@@ -1425,11 +1428,11 @@ AZ::Intersect::IntersectSegmentPolyhedron(
//DBG_Assert(iFirstPlane!=-1&&iLastPlane!=-1,("We have some bad border case to have only one plane, fix this function!"));
if (iFirstPlane == -1 && iLastPlane == -1)
{
return 0;
return false;
}
// A nonzero logical intersection, so the segment intersects the polyhedron
return 1;
return true;
}
//=========================================================================
@@ -1442,7 +1445,7 @@ AZ::Intersect::ClosestSegmentSegment(
const Vector3& segment2Start, const Vector3& segment2End,
float& segment1Proportion, float& segment2Proportion,
Vector3& closestPointSegment1, Vector3& closestPointSegment2,
float epsilon /*= 1e-4f*/ )
float epsilon)
{
const Vector3 segment1 = segment1End - segment1Start;
const Vector3 segment2 = segment2End - segment2Start;
Code/Framework/AzCore/AzCore/Math/IntersectSegment.h
+364 -284
View File
@@ -5,257 +5,262 @@
* SPDX-License-Identifier: Apache-2.0 OR MIT
*
*/
#ifndef AZCORE_MATH_SEGMENT_INTERSECTION_H
#define AZCORE_MATH_SEGMENT_INTERSECTION_H
#pragma once
#include <AzCore/Math/Vector3.h>
#include <AzCore/Math/Aabb.h>
#include <AzCore/Math/Obb.h>
#include <AzCore/Math/Plane.h>
/// \file isect_segment.h
#include <AzCore/Math/Vector3.h>
namespace AZ
{
namespace Intersect
{
//! LineToPointDistanceTime computes the time of the shortest distance from point 'p' to segment (s1,s2).
//! To calculate the point of intersection:
//! P = s1 + u (s2 - s1)
//! @param s1 segment start point
//! @param s2 segment end point
//! @param p point to find the closest time to.
//! @return time (on the segment) for the shortest distance from 'p' to (s1,s2) [0.0f (s1),1.0f (s2)]
inline float LineToPointDistanceTime(const Vector3& s1, const Vector3& s21, const Vector3& p)
{
// so u = (p.x - s1.x)*(s2.x - s1.x) + (p.y - s1.y)*(s2.y - s1.y) + (p.z-s1.z)*(s2.z-s1.z) / |s2-s1|^2
return s21.Dot(p - s1) / s21.Dot(s21);
}
/**
* LineToPointDistanceTime computes the time of the shortest distance from point 'p' to segment (s1,s2).
* To calculate the point of intersection:
* P = s1 + u (s2 - s1)
* @param s1 segment start point
* @param s2 segment end point
* @param p point to find the closest time to.
* @return time (on the segment) for the shortest distance from 'p' to (s1,s2) [0.0f (s1),1.0f (s2)]
*/
float LineToPointDistanceTime(const Vector3& s1, const Vector3& s21, const Vector3& p);
//! LineToPointDistance computes the closest point to 'p' from a segment (s1,s2).
//! @param s1 segment start point
//! @param s2 segment end point
//! @param p point to find the closest time to.
//! @param u time (on the segment) for the shortest distance from 'p' to (s1,s2) [0.0f (s1),1.0f (s2)]
//! @return the closest point
inline Vector3 LineToPointDistance(const Vector3& s1, const Vector3& s2, const Vector3& p, float& u)
{
const Vector3 s21 = s2 - s1;
// we assume seg1 and seg2 are NOT coincident
AZ_MATH_ASSERT(!s21.IsClose(Vector3(0.0f), 1e-4f), "OK we agreed that we will pass valid segments! (s1 != s2)");
/**
* LineToPointDistance computes the closest point to 'p' from a segment (s1,s2).
* @param s1 segment start point
* @param s2 segment end point
* @param p point to find the closest time to.
* @param u time (on the segment) for the shortest distance from 'p' to (s1,s2) [0.0f (s1),1.0f (s2)]
* @return the closest point
*/
Vector3 LineToPointDistance(const Vector3& s1, const Vector3& s2, const Vector3& p, float& u);
u = LineToPointDistanceTime(s1, s21, p);
return s1 + u * s21;
}
//! Given segment pq and triangle abc (CCW), returns whether segment intersects
//! triangle and if so, also returns the barycentric coordinates (u,v,w)
//! of the intersection point.
//! @param p segment start point
//! @param q segment end point
//! @param a triangle point 1
//! @param b triangle point 2
//! @param c triangle point 3
//! @param normal at the intersection point.
//! @param t time of intersection along the segment [0.0 (p), 1.0 (q)]
//! @return 1 if the segment intersects the triangle otherwise 0
/**
* Given segment pq and triangle abc (CCW), returns whether segment intersects
* triangle and if so, also returns the barycentric coordinates (u,v,w)
* of the intersection point.
*
* @param p segment start point
* @param q segment end point
* @param a triangle point 1
* @param b triangle point 2
* @param c triangle point 3
* @param normal at the intersection point.
* @param t time of intersection along the segment [0.0 (p), 1.0 (q)]
* @return true if the segments intersects the triangle otherwise false
*/
int IntersectSegmentTriangleCCW(
const Vector3& p, const Vector3& q, const Vector3& a, const Vector3& b, const Vector3& c,
/*float &u, float &v, float &w,*/ Vector3& normal, float& t);
const Vector3& p, const Vector3& q, const Vector3& a, const Vector3& b, const Vector3& c, Vector3& normal, float& t);
//! Same as \ref IntersectSegmentTriangleCCW without respecting the triangle (a,b,c) vertex order (double sided).
/**
* Same as \ref IntersectSegmentTriangleCCW without respecting the triangle (a,b,c) vertex order (double sided).
*
* @param p segment start point
* @param q segment end point
* @param a triangle point 1
* @param b triangle point 2
* @param c triangle point 3
* @param normal at the intersection point;
* @param t time of intersection along the segment [0.0 (p), 1.0 (q)]
* @return true if the segments intersects the triangle otherwise false
*/
int IntersectSegmentTriangle(
const Vector3& p, const Vector3& q, const Vector3& a, const Vector3& b, const Vector3& c,
/*float &u, float &v, float &w,*/ Vector3& normal, float& t);
const Vector3& p, const Vector3& q, const Vector3& a, const Vector3& b, const Vector3& c, Vector3& normal, float& t);
//! Ray aabb intersection result types.
enum RayAABBIsectTypes
enum RayAABBIsectTypes : AZ::s32
{
ISECT_RAY_AABB_NONE = 0, ///< no intersection
ISECT_RAY_AABB_SA_INSIDE, ///< the ray starts inside the aabb
ISECT_RAY_AABB_ISECT, ///< intersects along the PQ segment
ISECT_RAY_AABB_NONE = 0, ///< no intersection
ISECT_RAY_AABB_SA_INSIDE, ///< the ray starts inside the aabb
ISECT_RAY_AABB_ISECT, ///< intersects along the PQ segment
};
//! Intersect ray R(t) = rayStart + t*d against AABB a. When intersecting,
//! return intersection distance tmin and point q of intersection.
//! @param rayStart ray starting point
//! @param dir ray direction and length (dir = rayEnd - rayStart)
//! @param dirRCP 1/dir (reciprocal direction - we cache this result very often so we don't need to compute it multiple times, otherwise just use dir.GetReciprocal())
//! @param aabb Axis aligned bounding box to intersect against
//! @param tStart time on ray of the first intersection [0,1] or 0 if the ray starts inside the aabb - check the return value
//! @param tEnd time of the of the second intersection [0,1] (it can be > 1 if intersects after the rayEnd)
//! @param startNormal normal at the start point.
//! @return \ref RayAABBIsectTypes
int IntersectRayAABB(
const Vector3& rayStart, const Vector3& dir, const Vector3& dirRCP, const Aabb& aabb,
float& tStart, float& tEnd, Vector3& startNormal /*, Vector3& inter*/);
/**
* Intersect ray R(t) = rayStart + t*d against AABB a. When intersecting,
* return intersection distance tmin and point q of intersection.
* @param rayStart ray starting point
* @param dir ray direction and length (dir = rayEnd - rayStart)
* @param dirRCP 1/dir (reciprocal direction - we cache this result very often so we don't need to compute it multiple times,
* otherwise just use dir.GetReciprocal())
* @param aabb Axis aligned bounding box to intersect against
* @param tStart time on ray of the first intersection [0,1] or 0 if the ray starts inside the aabb - check the return value
* @param tEnd time of the of the second intersection [0,1] (it can be > 1 if intersects after the rayEnd)
* @param startNormal normal at the start point.
* @return \ref RayAABBIsectTypes
*/
RayAABBIsectTypes IntersectRayAABB(
const Vector3& rayStart,
const Vector3& dir,
const Vector3& dirRCP,
const Aabb& aabb,
float& tStart,
float& tEnd,
Vector3& startNormal /*, Vector3& inter*/);
//! Intersect ray against AABB.
//! @param rayStart ray starting point.
//! @param dir ray reciprocal direction.
//! @param aabb Axis aligned bounding box to intersect against.
//! @param start length on ray of the first intersection.
//! @param end length of the of the second intersection.
//! @return \ref RayAABBIsectTypes In this faster version than IntersectRayAABB we return only ISECT_RAY_AABB_NONE and ISECT_RAY_AABB_ISECT.
//! You can check yourself for that case.
int IntersectRayAABB2(
const Vector3& rayStart, const Vector3& dirRCP, const Aabb& aabb,
float& start, float& end);
/**
* Intersect ray against AABB.
*
* @param rayStart ray starting point.
* @param dir ray reciprocal direction.
* @param aabb Axis aligned bounding box to intersect against.
* @param start length on ray of the first intersection.
* @param end length of the of the second intersection.
* @return \ref RayAABBIsectTypes In this faster version than IntersectRayAABB we return only ISECT_RAY_AABB_NONE and ISECT_RAY_AABB_ISECT. You can check yourself for that case.
*/
RayAABBIsectTypes IntersectRayAABB2(const Vector3& rayStart, const Vector3& dirRCP, const Aabb& aabb, float& start, float& end);
//! Clip a ray to an aabb. return true if ray was clipped. The ray
//! can be inside so don't use the result if the ray intersect the box.
inline int ClipRayWithAabb(
const Aabb& aabb, Vector3& rayStart, Vector3& rayEnd, float& tClipStart, float& tClipEnd)
{
Vector3 startNormal;
float tStart, tEnd;
Vector3 dirLen = rayEnd - rayStart;
if (IntersectRayAABB(rayStart, dirLen, dirLen.GetReciprocal(), aabb, tStart, tEnd, startNormal) != ISECT_RAY_AABB_NONE)
{
// clip the ray with the box
if (tStart > 0.0f)
{
rayStart = rayStart + tStart * dirLen;
tClipStart = tStart;
}
if (tEnd < 1.0f)
{
rayEnd = rayStart + tEnd * dirLen;
tClipEnd = tEnd;
}
/**
* Clip a ray to an aabb. return true if ray was clipped. The ray
* can be inside so don't use the result if the ray intersect the box.
*
* @param aabb bounds
* @param rayStart the start of the ray
* @param rayEnd the end of the ray
* @param tClipStart[out] The proportion where the ray enterts the aabb
* @param tClipEnd[out] The proportion where the ray exits the aabb
* @return true ray was clipped else false
*/
bool ClipRayWithAabb(const Aabb& aabb, Vector3& rayStart, Vector3& rayEnd, float& tClipStart, float& tClipEnd);
return 1;
}
/**
* Test segment and aabb where the segment is defined by midpoint
* midPoint = (p1-p0) * 0.5f and half vector halfVector = p1 - midPoint.
* the aabb is at the origin and defined by half extents only.
*
* @param midPoint midpoint of a line segment
* @param halfVector half vector of an aabb
* @param aabbExtends the extends of a bounded box
* @return 1 if the intersect, otherwise 0.
*/
bool TestSegmentAABBOrigin(const Vector3& midPoint, const Vector3& halfVector, const Vector3& aabbExtends);
return 0;
}
//! Test segment and aabb where the segment is defined by midpoint
//! midPoint = (p1-p0) * 0.5f and half vector halfVector = p1 - midPoint.
//! the aabb is at the origin and defined by half extents only.
//! @return 1 if the intersect, otherwise 0.
int TestSegmentAABBOrigin(const Vector3& midPoint, const Vector3& halfVector, const Vector3& aabbExtends);
//! Test if segment specified by points p0 and p1 intersects AABB. \ref TestSegmentAABBOrigin
//! @return 1 if the segment and AABB intersect, otherwise 0.
inline int TestSegmentAABB(const Vector3& p0, const Vector3& p1, const Aabb& aabb)
{
Vector3 e = aabb.GetExtents();
Vector3 d = p1 - p0;
Vector3 m = p0 + p1 - aabb.GetMin() - aabb.GetMax();
return TestSegmentAABBOrigin(m, d, e);
}
/**
* Test if segment specified by points p0 and p1 intersects AABB. \ref TestSegmentAABBOrigin
*
* @param p0 point 1
* @param p1 point 2
* @param aabb bounded box
* @return true if the segment and AABB intersect, otherwise false.
*/
bool TestSegmentAABB(const Vector3& p0, const Vector3& p1, const Aabb& aabb);
//! Ray sphere intersection result types.
enum SphereIsectTypes
enum SphereIsectTypes : AZ::s32
{
ISECT_RAY_SPHERE_SA_INSIDE = -1, // the ray starts inside the cylinder
ISECT_RAY_SPHERE_NONE, // no intersection
ISECT_RAY_SPHERE_ISECT, // along the PQ segment
ISECT_RAY_SPHERE_NONE, // no intersection
ISECT_RAY_SPHERE_ISECT, // along the PQ segment
};
//! IntersectRaySphereOrigin
//! return time t>=0 but not limited, so if you check a segment make sure
//! t <= segmentLen
//! @param rayStart ray start point
//! @param rayDirNormalized ray direction normalized.
//! @param shereRadius sphere radius
//! @param time of closest intersection [0,+INF] in relation to the normalized direction.
//! @return \ref SphereIsectTypes
AZ_INLINE int IntersectRaySphereOrigin(
const Vector3& rayStart, const Vector3& rayDirNormalized,
const float sphereRadius, float& t)
{
Vector3 m = rayStart;
float b = m.Dot(rayDirNormalized);
float c = m.Dot(m) - sphereRadius * sphereRadius;
/**
* IntersectRaySphereOrigin
* return time t>=0 but not limited, so if you check a segment make sure
* t <= segmentLen
* @param rayStart ray start point
* @param rayDirNormalized ray direction normalized.
* @param shereRadius sphere radius
* @param time of closest intersection [0,+INF] in relation to the normalized direction.
* @return \ref SphereIsectTypes
**/
SphereIsectTypes IntersectRaySphereOrigin(
const Vector3& rayStart, const Vector3& rayDirNormalized, const float sphereRadius, float& t);
// Exit if r's origin outside s (c > 0)and r pointing away from s (b > 0)
if (c > 0.0f && b > 0.0f)
{
return ISECT_RAY_SPHERE_NONE;
}
float discr = b * b - c;
// A negative discriminant corresponds to ray missing sphere
if (discr < 0.0f)
{
return ISECT_RAY_SPHERE_NONE;
}
/**
* Intersect ray (rayStart,rayDirNormalized) and sphere (sphereCenter,sphereRadius) \ref IntersectRaySphereOrigin
*
* @param rayStart
* @param rayDirNormalized
* @param sphereCenter
* @param sphereRadius
* @param t
* @return int
*/
SphereIsectTypes IntersectRaySphere(
const Vector3& rayStart, const Vector3& rayDirNormalized, const Vector3& sphereCenter, const float sphereRadius, float& t);
// Ray now found to intersect sphere, compute smallest t value of intersection
t = -b - Sqrt(discr);
// If t is negative, ray started inside sphere so clamp t to zero
if (t < 0.0f)
{
// t = 0.0f;
return ISECT_RAY_SPHERE_SA_INSIDE; // no hit if inside
}
//q = p + t * d;
return ISECT_RAY_SPHERE_ISECT;
}
//! Intersect ray (rayStart,rayDirNormalized) and sphere (sphereCenter,sphereRadius) \ref IntersectRaySphereOrigin
inline int IntersectRaySphere(
const Vector3& rayStart, const Vector3& rayDirNormalized, const Vector3& sphereCenter, const float sphereRadius, float& t)
{
return IntersectRaySphereOrigin(rayStart - sphereCenter, rayDirNormalized, sphereRadius, t);
}
//! @param rayOrigin The origin of the ray to test.
//! @param rayDir The direction of the ray to test. It has to be unit length.
//! @param diskCenter Center point of the disk
//! @param diskRadius Radius of the disk
//! @param diskNormal A normal perpendicular to the disk
//! @param[out] t If returning 1 (indicating a hit), this contains distance from rayOrigin along the normalized rayDir that the hit occured at.
//! @return The number of intersecting points.
/**
* @param rayOrigin The origin of the ray to test.
* @param rayDir The direction of the ray to test. It has to be unit length.
* @param diskCenter Center point of the disk
* @param diskRadius Radius of the disk
* @param diskNormal A normal perpendicular to the disk
* @param[out] t If returning 1 (indicating a hit), this contains distance from rayOrigin along the normalized rayDir
* that the hit occured at.
* @return The number of intersecting points.
**/
int IntersectRayDisk(
const Vector3& rayOrigin, const Vector3& rayDir, const Vector3& diskCenter, const float diskRadius, const AZ::Vector3& diskNormal, float& t);
const Vector3& rayOrigin,
const Vector3& rayDir,
const Vector3& diskCenter,
const float diskRadius,
const AZ::Vector3& diskNormal,
float& t);
//! If there is only one intersecting point, the coefficient is stored in \ref t1.
//! @param rayOrigin The origin of the ray to test.
//! @param rayDir The direction of the ray to test. It has to be unit length.
//! @param cylinderEnd1 The center of the circle on one end of the cylinder.
//! @param cylinderDir The direction pointing from \ref cylinderEnd1 to the other end of the cylinder. It has to be unit length.
//! @param cylinderHeight The distance between two centers of the circles on two ends of the cylinder respectively.
//! @param[out] t1 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated as "rayOrigin + t1 * rayDir".
//! @param[out] t2 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated as "rayOrigin + t2 * rayDir".
//! @return The number of intersecting points.
/**
* If there is only one intersecting point, the coefficient is stored in \ref t1.
* @param rayOrigin The origin of the ray to test.
* @param rayDir The direction of the ray to test. It has to be unit length.
* @param cylinderEnd1 The center of the circle on one end of the cylinder.
* @param cylinderDir The direction pointing from \ref cylinderEnd1 to the other end of the cylinder. It has to be unit
* length.
* @param cylinderHeight The distance between two centers of the circles on two ends of the cylinder respectively.
* @param[out] t1 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated
* as "rayOrigin + t1 * rayDir".
* @param[out] t2 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated
* as "rayOrigin + t2 * rayDir".
* @return The number of intersecting points.
**/
int IntersectRayCappedCylinder(
const Vector3& rayOrigin, const Vector3& rayDir,
const Vector3& cylinderEnd1, const Vector3& cylinderDir, float cylinderHeight, float cylinderRadius,
float& t1, float& t2);
const Vector3& rayOrigin,
const Vector3& rayDir,
const Vector3& cylinderEnd1,
const Vector3& cylinderDir,
float cylinderHeight,
float cylinderRadius,
float& t1,
float& t2);
//! If there is only one intersecting point, the coefficient is stored in \ref t1.
//! @param rayOrigin The origin of the ray to test.
//! @param rayDir The direction of the ray to test. It has to be unit length.
//! @param coneApex The apex of the cone.
//! @param coneDir The unit-length direction from the apex to the base.
//! @param coneHeight The height of the cone, from the apex to the base.
//! @param coneBaseRadius The radius of the cone base circle.
//! @param[out] t1 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated as "rayOrigin + t1 * rayDir".
//! @param[out] t2 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated as "rayOrigin + t2 * rayDir".
//! @return The number of intersecting points.
/**
* If there is only one intersecting point, the coefficient is stored in \ref t1.
* @param rayOrigin The origin of the ray to test.
* @param rayDir The direction of the ray to test. It has to be unit length.
* @param coneApex The apex of the cone.
* @param coneDir The unit-length direction from the apex to the base.
* @param coneHeight The height of the cone, from the apex to the base.
* @param coneBaseRadius The radius of the cone base circle.
* @param[out] t1 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated
* as "rayOrigin + t1 * rayDir".
* @param[out] t2 A possible coefficient in the ray's explicit equation from which an intersecting point is calculated
* as "rayOrigin + t2 * rayDir".
* @return The number of intersecting points.
**/
int IntersectRayCone(
const Vector3& rayOrigin, const Vector3& rayDir,
const Vector3& coneApex, const Vector3& coneDir, float coneHeight, float coneBaseRadius,
float& t1, float& t2);
const Vector3& rayOrigin,
const Vector3& rayDir,
const Vector3& coneApex,
const Vector3& coneDir,
float coneHeight,
float coneBaseRadius,
float& t1,
float& t2);
//! Test intersection between a ray and a plane in 3D.
//! @param rayOrigin The origin of the ray to test intersection with.
//! @param rayDir The direction of the ray to test intersection with.
//! @param planePos A point on the plane to test intersection with.
//! @param planeNormal The normal of the plane to test intersection with.
//! @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin + t * rayDirection".
//! @return The number of intersection point.
/**
* Test intersection between a ray and a plane in 3D.
* @param rayOrigin The origin of the ray to test intersection with.
* @param rayDir The direction of the ray to test intersection with.
* @param planePos A point on the plane to test intersection with.
* @param planeNormal The normal of the plane to test intersection with.
* @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin
*+ t * rayDirection".
* @return The number of intersection point.
**/
int IntersectRayPlane(
const Vector3& rayOrigin, const Vector3& rayDir, const Vector3& planePos,
const Vector3& planeNormal, float& t);
const Vector3& rayOrigin, const Vector3& rayDir, const Vector3& planePos, const Vector3& planeNormal, float& t);
//! Test intersection between a ray and a two-sided quadrilateral defined by four points in 3D.
//! The four points that define the quadrilateral could be passed in with either counter clock-wise
//! The four points that define the quadrilateral could be passed in with either counter clock-wise
//! winding or clock-wise winding.
//! @param rayOrigin The origin of the ray to test intersection with.
//! @param rayDir The direction of the ray to test intersection with.
@@ -263,105 +268,180 @@ namespace AZ
//! @param vertexB One of the four points that define the quadrilateral.
//! @param vertexC One of the four points that define the quadrilateral.
//! @param vertexD One of the four points that define the quadrilateral.
//! @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin + t * rayDirection".
//! @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin +
//! t * rayDirection".
//! @return The number of intersection point.
int IntersectRayQuad(
const Vector3& rayOrigin, const Vector3& rayDir, const Vector3& vertexA,
const Vector3& vertexB, const Vector3& vertexC, const Vector3& vertexD, float& t);
//! Test intersection between a ray and an oriented box in 3D.
//! @param rayOrigin The origin of the ray to test intersection with.
//! @param rayDir The direction of the ray to test intersection with.
//! @param boxCenter The position of the center of the box.
//! @param boxAxis1 An axis along one dimension of the oriented box.
//! @param boxAxis2 An axis along one dimension of the oriented box.
//! @param boxAxis3 An axis along one dimension of the oriented box.
//! @param boxHalfExtent1 The half extent of the box on the dimension of \ref boxAxis1.
//! @param boxHalfExtent2 The half extent of the box on the dimension of \ref boxAxis2.
//! @param boxHalfExtent3 The half extent of the box on the dimension of \ref boxAxis3.
//! @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin + t * rayDirection".
//! @return 1 if there is an intersection, 0 otherwise.
int IntersectRayBox(
const Vector3& rayOrigin, const Vector3& rayDir, const Vector3& boxCenter, const Vector3& boxAxis1,
const Vector3& boxAxis2, const Vector3& boxAxis3, float boxHalfExtent1, float boxHalfExtent2, float boxHalfExtent3,
const Vector3& rayOrigin,
const Vector3& rayDir,
const Vector3& vertexA,
const Vector3& vertexB,
const Vector3& vertexC,
const Vector3& vertexD,
float& t);
//! Test intersection between a ray and an OBB.
//! @param rayOrigin The origin of the ray to test intersection with.
//! @param rayDir The direction of the ray to test intersection with.
//! @param obb The OBB to test for intersection with the ray.
//! @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin + t * rayDirection".
//! @return 1 if there is an intersection, 0 otherwise.
/** Test intersection between a ray and an oriented box in 3D.
* @param rayOrigin The origin of the ray to test intersection with.
* @param rayDir The direction of the ray to test intersection with.
* @param boxCenter The position of the center of the box.
* @param boxAxis1 An axis along one dimension of the oriented box.
* @param boxAxis2 An axis along one dimension of the oriented box.
* @param boxAxis3 An axis along one dimension of the oriented box.
* @param boxHalfExtent1 The half extent of the box on the dimension of \ref boxAxis1.
* @param boxHalfExtent2 The half extent of the box on the dimension of \ref boxAxis2.
* @param boxHalfExtent3 The half extent of the box on the dimension of \ref boxAxis3.
* @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin +
* t * rayDirection".
* @return 1 if there is an intersection, 0 otherwise.
**/
int IntersectRayBox(
const Vector3& rayOrigin,
const Vector3& rayDir,
const Vector3& boxCenter,
const Vector3& boxAxis1,
const Vector3& boxAxis2,
const Vector3& boxAxis3,
float boxHalfExtent1,
float boxHalfExtent2,
float boxHalfExtent3,
float& t);
/**
* Test intersection between a ray and an OBB.
* @param rayOrigin The origin of the ray to test intersection with.
* @param rayDir The direction of the ray to test intersection with.
* @param obb The OBB to test for intersection with the ray.
* @param t[out] The coefficient in the ray's explicit equation from which the intersecting point is calculated as "rayOrigin + t *
* rayDirection".
* @return 1 if there is an intersection, 0 otherwise.
*/
int IntersectRayObb(const Vector3& rayOrigin, const Vector3& rayDir, const Obb& obb, float& t);
//! Ray cylinder intersection types.
enum CylinderIsectTypes
enum CylinderIsectTypes : AZ::s32
{
RR_ISECT_RAY_CYL_SA_INSIDE = -1, // the ray starts inside the cylinder
RR_ISECT_RAY_CYL_NONE, // no intersection
RR_ISECT_RAY_CYL_PQ, // along the PQ segment
RR_ISECT_RAY_CYL_P_SIDE, // on the P side
RR_ISECT_RAY_CYL_Q_SIDE, // on the Q side
RR_ISECT_RAY_CYL_NONE, // no intersection
RR_ISECT_RAY_CYL_PQ, // along the PQ segment
RR_ISECT_RAY_CYL_P_SIDE, // on the P side
RR_ISECT_RAY_CYL_Q_SIDE, // on the Q side
};
//! Intersect segment S(t)=sa+t(dir), 0<=t<=1 against cylinder specified by p, q and r.
int IntersectSegmentCylinder(
const Vector3& sa, const Vector3& dir, const Vector3& p, const Vector3& q,
const float r, float& t);
/**
* Reference: Real-Time Collision Detection - 5.3.7 Intersecting Ray or Segment Against Cylinder
* Intersect segment S(t)=sa+t(dir), 0<=t<=1 against cylinder specified by p, q and r.
*
* @param sa point
* @param dir magnitude along sa
* @param p center point of side 1 cylinder
* @param q center point of side 2 cylinder
* @param r radius of cylinder
* @param t[out] proporition along line semgnet
* @return CylinderIsectTypes
*/
CylinderIsectTypes IntersectSegmentCylinder(
const Vector3& sa, const Vector3& dir, const Vector3& p, const Vector3& q, const float r, float& t);
//! Capsule ray intersect types.
enum CapsuleIsectTypes
{
ISECT_RAY_CAPSULE_SA_INSIDE = -1, // the ray starts inside the cylinder
ISECT_RAY_CAPSULE_NONE, // no intersection
ISECT_RAY_CAPSULE_PQ, // along the PQ segment
ISECT_RAY_CAPSULE_P_SIDE, // on the P side
ISECT_RAY_CAPSULE_Q_SIDE, // on the Q side
ISECT_RAY_CAPSULE_PQ, // along the PQ segment
ISECT_RAY_CAPSULE_P_SIDE, // on the P side
ISECT_RAY_CAPSULE_Q_SIDE, // on the Q side
};
//! This is a quick implementation of segment capsule based on segment cylinder \ref IntersectSegmentCylinder
//! segment sphere intersection. We can optimize it a lot once we fix the ray
//! cylinder intersection.
int IntersectSegmentCapsule(
const Vector3& sa, const Vector3& dir, const Vector3& p,
const Vector3& q, const float r, float& t);
/**
* This is a quick implementation of segment capsule based on segment cylinder \ref IntersectSegmentCylinder
* segment sphere intersection. We can optimize it a lot once we fix the ray
* cylinder intersection.
*/
CapsuleIsectTypes IntersectSegmentCapsule(
const Vector3& sa, const Vector3& dir, const Vector3& p, const Vector3& q, const float r, float& t);
//! Intersect segment S(t)=A+t(B-A), 0<=t<=1 against convex polyhedron specified
//! by the n halfspaces defined by the planes p[]. On exit tfirst and tlast
//! define the intersection, if any.
int IntersectSegmentPolyhedron(
const Vector3& sa, const Vector3& sBA, const Plane p[], int numPlanes,
float& tfirst, float& tlast, int& iFirstPlane, int& iLastPlane);
/**
* Intersect segment S(t)=A+t(B-A), 0<=t<=1 against convex polyhedron specified
* by the n halfspaces defined by the planes p[]. On exit tfirst and tlast
* define the intersection, if any.
*/
bool IntersectSegmentPolyhedron(
const Vector3& sa,
const Vector3& sBA,
const Plane p[],
int numPlanes,
float& tfirst,
float& tlast,
int& iFirstPlane,
int& iLastPlane);
//! Calculate the line segment closestPointSegment1<->closestPointSegment2 that is the shortest route between
//! two segments segment1Start<->segment1End and segment2Start<->segment2End. Also calculate the values of segment1Proportion and segment2Proportion where
//! closestPointSegment1 = segment1Start + (segment1Proportion * (segment1End - segment1Start))
//! closestPointSegment2 = segment2Start + (segment2Proportion * (segment2End - segment2Start))
//! If segments are parallel returns a solution.
/**
* Calculate the line segment closestPointSegment1<->closestPointSegment2 that is the shortest route between
* two segments segment1Start<->segment1End and segment2Start<->segment2End. Also calculate the values of segment1Proportion and
* segment2Proportion where closestPointSegment1 = segment1Start + (segment1Proportion * (segment1End - segment1Start))
* closestPointSegment2 = segment2Start + (segment2Proportion * (segment2End - segment2Start))
* If segments are parallel returns a solution.
* @param segment1Start start of segment 1.
* @param segment1End end of segment 1.
* @param segment2Start start of segment 2.
* @param segment2End end of segment 2.
* @param segment1Proportion[out] the proporition along segment 1 [0..1]
* @param segment2Proportion[out] the proporition along segment 2 [0..1]
* @param closestPointSegment1[out] closest point on segment 1.
* @param closestPointSegment2[out] closest point on segment 2.
* @param epsilon the minimum square distance where a line segment can be treated as a single point.
*/
void ClosestSegmentSegment(
const Vector3& segment1Start, const Vector3& segment1End,
const Vector3& segment2Start, const Vector3& segment2End,
float& segment1Proportion, float& segment2Proportion,
Vector3& closestPointSegment1, Vector3& closestPointSegment2,
const Vector3& segment1Start,
const Vector3& segment1End,
const Vector3& segment2Start,
const Vector3& segment2End,
float& segment1Proportion,
float& segment2Proportion,
Vector3& closestPointSegment1,
Vector3& closestPointSegment2,
float epsilon = 1e-4f);
//! Calculate the line segment closestPointSegment1<->closestPointSegment2 that is the shortest route between
//! two segments segment1Start<->segment1End and segment2Start<->segment2End.
//! If segments are parallel returns a solution.
/**
* Calculate the line segment closestPointSegment1<->closestPointSegment2 that is the shortest route between
* two segments segment1Start<->segment1End and segment2Start<->segment2End.
* If segments are parallel returns a solution.
*
* @param segment1Start start of segment 1.
* @param segment1End end of segment 1.
* @param segment2Start start of segment 2.
* @param segment2End end of segment 2.
* @param closestPointSegment1[out] closest point on segment 1.
* @param closestPointSegment2[out] closest point on segment 2.
* @param epsilon the minimum square distance where a line segment can be treated as a single point.
*/
void ClosestSegmentSegment(
const Vector3& segment1Start, const Vector3& segment1End,
const Vector3& segment2Start, const Vector3& segment2End,
Vector3& closestPointSegment1, Vector3& closestPointSegment2,
const Vector3& segment1Start,
const Vector3& segment1End,
const Vector3& segment2Start,
const Vector3& segment2End,
Vector3& closestPointSegment1,
Vector3& closestPointSegment2,
float epsilon = 1e-4f);
//! Calculate the point (closestPointOnSegment) that is the closest point on
//! segment segmentStart/segmentEnd to point. Also calculate the value of proportion where
//! closestPointOnSegment = segmentStart + (proportion * (segmentEnd - segmentStart))
/**
* Calculate the point (closestPointOnSegment) that is the closest point on
* segment segmentStart/segmentEnd to point. Also calculate the value of proportion where
* closestPointOnSegment = segmentStart + (proportion * (segmentEnd - segmentStart))
*
* @param point the point to test
* @param segmentStart the start of the segment
* @param segmentEnd the end of the segment
* @param proportion[out] the proportion of the segment L(t) = (end - start) * t
* @param closestPointOnSegment[out] the point along the line segment
*/
void ClosestPointSegment(
const Vector3& point, const Vector3& segmentStart, const Vector3& segmentEnd,
float& proportion, Vector3& closestPointOnSegment);
}
}
const Vector3& point,
const Vector3& segmentStart,
const Vector3& segmentEnd,
float& proportion,
Vector3& closestPointOnSegment);
} // namespace Intersect
} // namespace AZ
#endif // AZCORE_MATH_SEGMENT_INTERSECTION_H
#pragma once
#include <AzCore/Math/IntersectSegment.inl>
Code/Framework/AzCore/AzCore/Math/IntersectSegment.inl
+102
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@@ -0,0 +1,102 @@
/*
* Copyright (c) Contributors to the Open 3D Engine Project.
* For complete copyright and license terms please see the LICENSE at the root of this distribution.
*
* SPDX-License-Identifier: Apache-2.0 OR MIT
*
*/
#pragma once
namespace AZ
{
namespace Intersect
{
AZ_MATH_INLINE bool ClipRayWithAabb(const Aabb& aabb, Vector3& rayStart, Vector3& rayEnd, float& tClipStart, float& tClipEnd)
{
Vector3 startNormal;
float tStart, tEnd;
Vector3 dirLen = rayEnd - rayStart;
if (IntersectRayAABB(rayStart, dirLen, dirLen.GetReciprocal(), aabb, tStart, tEnd, startNormal) != ISECT_RAY_AABB_NONE)
{
// clip the ray with the box
if (tStart > 0.0f)
{
rayStart = rayStart + tStart * dirLen;
tClipStart = tStart;
}
if (tEnd < 1.0f)
{
rayEnd = rayStart + tEnd * dirLen;
tClipEnd = tEnd;
}
return true;
}
return false;
}
AZ_MATH_INLINE SphereIsectTypes
IntersectRaySphereOrigin(const Vector3& rayStart, const Vector3& rayDirNormalized, const float sphereRadius, float& t)
{
Vector3 m = rayStart;
float b = m.Dot(rayDirNormalized);
float c = m.Dot(m) - sphereRadius * sphereRadius;
// Exit if r's origin outside s (c > 0)and r pointing away from s (b > 0)
if (c > 0.0f && b > 0.0f)
{
return ISECT_RAY_SPHERE_NONE;
}
float discr = b * b - c;
// A negative discriminant corresponds to ray missing sphere
if (discr < 0.0f)
{
return ISECT_RAY_SPHERE_NONE;
}
// Ray now found to intersect sphere, compute smallest t value of intersection
t = -b - Sqrt(discr);
// If t is negative, ray started inside sphere so clamp t to zero
if (t < 0.0f)
{
// t = 0.0f;
return ISECT_RAY_SPHERE_SA_INSIDE; // no hit if inside
}
// q = p + t * d;
return ISECT_RAY_SPHERE_ISECT;
}
AZ_MATH_INLINE SphereIsectTypes IntersectRaySphere(const Vector3& rayStart, const Vector3& rayDirNormalized, const Vector3& sphereCenter, const float sphereRadius, float& t)
{
return IntersectRaySphereOrigin(rayStart - sphereCenter, rayDirNormalized, sphereRadius, t);
}
AZ_MATH_INLINE Vector3 LineToPointDistance(const Vector3& s1, const Vector3& s2, const Vector3& p, float& u)
{
const Vector3 s21 = s2 - s1;
// we assume seg1 and seg2 are NOT coincident
AZ_MATH_ASSERT(!s21.IsClose(Vector3(0.0f), 1e-4f), "OK we agreed that we will pass valid segments! (s1 != s2)");
u = LineToPointDistanceTime(s1, s21, p);
return s1 + u * s21;
}
AZ_MATH_INLINE float LineToPointDistanceTime(const Vector3& s1, const Vector3& s21, const Vector3& p)
{
// so u = (p.x - s1.x)*(s2.x - s1.x) + (p.y - s1.y)*(s2.y - s1.y) + (p.z-s1.z)*(s2.z-s1.z) / |s2-s1|^2
return s21.Dot(p - s1) / s21.Dot(s21);
}
AZ_MATH_INLINE bool TestSegmentAABB(const Vector3& p0, const Vector3& p1, const Aabb& aabb)
{
Vector3 e = aabb.GetExtents();
Vector3 d = p1 - p0;
Vector3 m = p0 + p1 - aabb.GetMin() - aabb.GetMax();
return TestSegmentAABBOrigin(m, d, e);
}
} // namespace Intersect
} // namespace AZ
Code/Framework/AzCore/AzCore/azcore_files.cmake
+1
View File
@@ -282,6 +282,7 @@ set(FILES
Math/Internal/VertexContainer.inl
Math/InterpolationSample.h
Math/IntersectPoint.h
Math/IntersectSegment.inl
Math/IntersectSegment.cpp
Math/IntersectSegment.h
Math/MathIntrinsics.h