280 lines
9.9 KiB
C++
280 lines
9.9 KiB
C++
// Copyright (C) 2002-2012 Nikolaus Gebhardt
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// This file is part of the "Irrlicht Engine".
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// For conditions of distribution and use, see copyright notice in irrlicht.h
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#ifndef __IRR_TRIANGLE_3D_H_INCLUDED__
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#define __IRR_TRIANGLE_3D_H_INCLUDED__
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#include "vector3d.h"
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#include "line3d.h"
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#include "plane3d.h"
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#include "aabbox3d.h"
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namespace irr
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{
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namespace core
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{
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//! 3d triangle template class for doing collision detection and other things.
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template <class T>
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class triangle3d
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{
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public:
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//! Constructor for an all 0 triangle
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triangle3d() {}
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//! Constructor for triangle with given three vertices
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triangle3d(vector3d<T> v1, vector3d<T> v2, vector3d<T> v3) : pointA(v1), pointB(v2), pointC(v3) {}
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//! Equality operator
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bool operator==(const triangle3d<T>& other) const
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{
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return other.pointA==pointA && other.pointB==pointB && other.pointC==pointC;
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}
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//! Inequality operator
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bool operator!=(const triangle3d<T>& other) const
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{
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return !(*this==other);
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}
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//! Determines if the triangle is totally inside a bounding box.
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/** \param box Box to check.
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\return True if triangle is within the box, otherwise false. */
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bool isTotalInsideBox(const aabbox3d<T>& box) const
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{
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return (box.isPointInside(pointA) &&
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box.isPointInside(pointB) &&
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box.isPointInside(pointC));
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}
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//! Determines if the triangle is totally outside a bounding box.
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/** \param box Box to check.
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\return True if triangle is outside the box, otherwise false. */
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bool isTotalOutsideBox(const aabbox3d<T>& box) const
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{
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return ((pointA.X > box.MaxEdge.X && pointB.X > box.MaxEdge.X && pointC.X > box.MaxEdge.X) ||
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(pointA.Y > box.MaxEdge.Y && pointB.Y > box.MaxEdge.Y && pointC.Y > box.MaxEdge.Y) ||
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(pointA.Z > box.MaxEdge.Z && pointB.Z > box.MaxEdge.Z && pointC.Z > box.MaxEdge.Z) ||
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(pointA.X < box.MinEdge.X && pointB.X < box.MinEdge.X && pointC.X < box.MinEdge.X) ||
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(pointA.Y < box.MinEdge.Y && pointB.Y < box.MinEdge.Y && pointC.Y < box.MinEdge.Y) ||
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(pointA.Z < box.MinEdge.Z && pointB.Z < box.MinEdge.Z && pointC.Z < box.MinEdge.Z));
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}
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//! Get the closest point on a triangle to a point on the same plane.
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/** \param p Point which must be on the same plane as the triangle.
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\return The closest point of the triangle */
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core::vector3d<T> closestPointOnTriangle(const core::vector3d<T>& p) const
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{
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const core::vector3d<T> rab = line3d<T>(pointA, pointB).getClosestPoint(p);
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const core::vector3d<T> rbc = line3d<T>(pointB, pointC).getClosestPoint(p);
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const core::vector3d<T> rca = line3d<T>(pointC, pointA).getClosestPoint(p);
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const T d1 = rab.getDistanceFrom(p);
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const T d2 = rbc.getDistanceFrom(p);
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const T d3 = rca.getDistanceFrom(p);
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if (d1 < d2)
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return d1 < d3 ? rab : rca;
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return d2 < d3 ? rbc : rca;
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}
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//! Check if a point is inside the triangle (border-points count also as inside)
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/*
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\param p Point to test. Assumes that this point is already
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on the plane of the triangle.
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\return True if the point is inside the triangle, otherwise false. */
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bool isPointInside(const vector3d<T>& p) const
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{
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vector3d<f64> af64((f64)pointA.X, (f64)pointA.Y, (f64)pointA.Z);
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vector3d<f64> bf64((f64)pointB.X, (f64)pointB.Y, (f64)pointB.Z);
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vector3d<f64> cf64((f64)pointC.X, (f64)pointC.Y, (f64)pointC.Z);
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vector3d<f64> pf64((f64)p.X, (f64)p.Y, (f64)p.Z);
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return (isOnSameSide(pf64, af64, bf64, cf64) &&
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isOnSameSide(pf64, bf64, af64, cf64) &&
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isOnSameSide(pf64, cf64, af64, bf64));
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}
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//! Check if a point is inside the triangle (border-points count also as inside)
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/** This method uses a barycentric coordinate system.
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It is faster than isPointInside but is more susceptible to floating point rounding
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errors. This will especially be noticable when the FPU is in single precision mode
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(which is for example set on default by Direct3D).
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\param p Point to test. Assumes that this point is already
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on the plane of the triangle.
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\return True if point is inside the triangle, otherwise false. */
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bool isPointInsideFast(const vector3d<T>& p) const
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{
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const vector3d<T> a = pointC - pointA;
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const vector3d<T> b = pointB - pointA;
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const vector3d<T> c = p - pointA;
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const f64 dotAA = a.dotProduct( a);
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const f64 dotAB = a.dotProduct( b);
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const f64 dotAC = a.dotProduct( c);
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const f64 dotBB = b.dotProduct( b);
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const f64 dotBC = b.dotProduct( c);
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// get coordinates in barycentric coordinate system
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const f64 invDenom = 1/(dotAA * dotBB - dotAB * dotAB);
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const f64 u = (dotBB * dotAC - dotAB * dotBC) * invDenom;
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const f64 v = (dotAA * dotBC - dotAB * dotAC ) * invDenom;
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// We count border-points as inside to keep downward compatibility.
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// Rounding-error also needed for some test-cases.
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return (u > -ROUNDING_ERROR_f32) && (v >= 0) && (u + v < 1+ROUNDING_ERROR_f32);
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}
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//! Get an intersection with a 3d line.
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/** \param line Line to intersect with.
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\param outIntersection Place to store the intersection point, if there is one.
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\return True if there was an intersection, false if not. */
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bool getIntersectionWithLimitedLine(const line3d<T>& line,
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vector3d<T>& outIntersection) const
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{
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return getIntersectionWithLine(line.start,
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line.getVector(), outIntersection) &&
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outIntersection.isBetweenPoints(line.start, line.end);
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}
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//! Get an intersection with a 3d line.
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/** Please note that also points are returned as intersection which
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are on the line, but not between the start and end point of the line.
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If you want the returned point be between start and end
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use getIntersectionWithLimitedLine().
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\param linePoint Point of the line to intersect with.
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\param lineVect Vector of the line to intersect with.
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\param outIntersection Place to store the intersection point, if there is one.
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\return True if there was an intersection, false if there was not. */
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bool getIntersectionWithLine(const vector3d<T>& linePoint,
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const vector3d<T>& lineVect, vector3d<T>& outIntersection) const
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{
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if (getIntersectionOfPlaneWithLine(linePoint, lineVect, outIntersection))
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return isPointInside(outIntersection);
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return false;
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}
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//! Calculates the intersection between a 3d line and the plane the triangle is on.
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/** \param lineVect Vector of the line to intersect with.
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\param linePoint Point of the line to intersect with.
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\param outIntersection Place to store the intersection point, if there is one.
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\return True if there was an intersection, else false. */
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bool getIntersectionOfPlaneWithLine(const vector3d<T>& linePoint,
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const vector3d<T>& lineVect, vector3d<T>& outIntersection) const
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{
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// Work with f64 to get more precise results (makes enough difference to be worth the casts).
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const vector3d<f64> linePointf64(linePoint.X, linePoint.Y, linePoint.Z);
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const vector3d<f64> lineVectf64(lineVect.X, lineVect.Y, lineVect.Z);
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vector3d<f64> outIntersectionf64;
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core::triangle3d<irr::f64> trianglef64(vector3d<f64>((f64)pointA.X, (f64)pointA.Y, (f64)pointA.Z)
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,vector3d<f64>((f64)pointB.X, (f64)pointB.Y, (f64)pointB.Z)
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, vector3d<f64>((f64)pointC.X, (f64)pointC.Y, (f64)pointC.Z));
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const vector3d<irr::f64> normalf64 = trianglef64.getNormal().normalize();
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f64 t2;
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if ( core::iszero ( t2 = normalf64.dotProduct(lineVectf64) ) )
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return false;
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f64 d = trianglef64.pointA.dotProduct(normalf64);
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f64 t = -(normalf64.dotProduct(linePointf64) - d) / t2;
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outIntersectionf64 = linePointf64 + (lineVectf64 * t);
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outIntersection.X = (T)outIntersectionf64.X;
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outIntersection.Y = (T)outIntersectionf64.Y;
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outIntersection.Z = (T)outIntersectionf64.Z;
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return true;
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}
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//! Get the normal of the triangle.
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/** Please note: The normal is not always normalized. */
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vector3d<T> getNormal() const
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{
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return (pointB - pointA).crossProduct(pointC - pointA);
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}
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//! Test if the triangle would be front or backfacing from any point.
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/** Thus, this method assumes a camera position from which the
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triangle is definitely visible when looking at the given direction.
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Do not use this method with points as it will give wrong results!
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\param lookDirection Look direction.
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\return True if the plane is front facing and false if it is backfacing. */
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bool isFrontFacing(const vector3d<T>& lookDirection) const
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{
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const vector3d<T> n = getNormal().normalize();
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const f32 d = (f32)n.dotProduct(lookDirection);
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return F32_LOWER_EQUAL_0(d);
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}
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//! Get the plane of this triangle.
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plane3d<T> getPlane() const
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{
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return plane3d<T>(pointA, pointB, pointC);
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}
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//! Get the area of the triangle
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T getArea() const
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{
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return (pointB - pointA).crossProduct(pointC - pointA).getLength() * 0.5f;
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}
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//! sets the triangle's points
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void set(const core::vector3d<T>& a, const core::vector3d<T>& b, const core::vector3d<T>& c)
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{
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pointA = a;
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pointB = b;
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pointC = c;
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}
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//! the three points of the triangle
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vector3d<T> pointA;
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vector3d<T> pointB;
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vector3d<T> pointC;
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private:
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// Using f64 instead of <T> to avoid integer overflows when T=int (maybe also less floating point troubles).
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bool isOnSameSide(const vector3d<f64>& p1, const vector3d<f64>& p2,
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const vector3d<f64>& a, const vector3d<f64>& b) const
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{
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vector3d<f64> bminusa = b - a;
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vector3d<f64> cp1 = bminusa.crossProduct(p1 - a);
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vector3d<f64> cp2 = bminusa.crossProduct(p2 - a);
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f64 res = cp1.dotProduct(cp2);
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if ( res < 0 )
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{
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// This catches some floating point troubles.
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// Unfortunately slightly expensive and we don't really know the best epsilon for iszero.
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vector3d<f64> cp1 = bminusa.normalize().crossProduct((p1 - a).normalize());
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if ( core::iszero(cp1.X, (f64)ROUNDING_ERROR_f32)
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&& core::iszero(cp1.Y, (f64)ROUNDING_ERROR_f32)
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&& core::iszero(cp1.Z, (f64)ROUNDING_ERROR_f32) )
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{
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res = 0.f;
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}
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}
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return (res >= 0.0f);
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}
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};
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//! Typedef for a f32 3d triangle.
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typedef triangle3d<f32> triangle3df;
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//! Typedef for an integer 3d triangle.
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typedef triangle3d<s32> triangle3di;
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} // end namespace core
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} // end namespace irr
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#endif
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