///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Contains AABB-related code.
* \file IceAABB.cpp
* \author Pierre Terdiman
* \date January, 29, 2000
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* AABB class.
* \class AABB
* \author Pierre Terdiman
* \version 1.0
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Precompiled Header
#include "Stdafx.h"
using namespace IceMaths;
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Computes the sum of two AABBs.
* \param aabb [in] the other AABB
* \return Self-Reference
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
AABB& AABB::Add(const AABB& aabb)
{
// Compute new min & max values
Point Min; GetMin(Min);
Point Tmp; aabb.GetMin(Tmp);
Min.Min(Tmp);
Point Max; GetMax(Max);
aabb.GetMax(Tmp);
Max.Max(Tmp);
// Update this
SetMinMax(Min, Max);
return *this;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Makes a cube from the AABB.
* \param cube [out] the cube AABB
* \return cube edge length
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
float AABB::MakeCube(AABB& cube) const
{
Point Ext; GetExtents(Ext);
float Max = Ext.Max();
Point Cnt; GetCenter(Cnt);
cube.SetCenterExtents(Cnt, Point(Max, Max, Max));
return Max;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Makes a sphere from the AABB.
* \param sphere [out] sphere containing the AABB
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void AABB::MakeSphere(Sphere& sphere) const
{
GetExtents(sphere.mCenter);
sphere.mRadius = sphere.mCenter.Magnitude() * 1.00001f; // To make sure sphere::Contains(*this) succeeds
GetCenter(sphere.mCenter);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Checks a box is inside another box.
* \param box [in] the other AABB
* \return true if current box is inside input box
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool AABB::IsInside(const AABB& box) const
{
if(box.GetMin(0)>GetMin(0)) return false;
if(box.GetMin(1)>GetMin(1)) return false;
if(box.GetMin(2)>GetMin(2)) return false;
if(box.GetMax(0)<GetMax(0)) return false;
if(box.GetMax(1)<GetMax(1)) return false;
if(box.GetMax(2)<GetMax(2)) return false;
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Computes the AABB planes.
* \param planes [out] 6 planes surrounding the box
* \return true if success
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool AABB::ComputePlanes(Plane* planes) const
{
// Checkings
if(!planes) return false;
Point Center, Extents;
GetCenter(Center);
GetExtents(Extents);
// Writes normals
planes[0].n = Point(1.0f, 0.0f, 0.0f);
planes[1].n = Point(-1.0f, 0.0f, 0.0f);
planes[2].n = Point(0.0f, 1.0f, 0.0f);
planes[3].n = Point(0.0f, -1.0f, 0.0f);
planes[4].n = Point(0.0f, 0.0f, 1.0f);
planes[5].n = Point(0.0f, 0.0f, -1.0f);
// Compute a point on each plane
Point p0 = Point(Center.x+Extents.x, Center.y, Center.z);
Point p1 = Point(Center.x-Extents.x, Center.y, Center.z);
Point p2 = Point(Center.x, Center.y+Extents.y, Center.z);
Point p3 = Point(Center.x, Center.y-Extents.y, Center.z);
Point p4 = Point(Center.x, Center.y, Center.z+Extents.z);
Point p5 = Point(Center.x, Center.y, Center.z-Extents.z);
// Compute d
planes[0].d = -(planes[0].n|p0);
planes[1].d = -(planes[1].n|p1);
planes[2].d = -(planes[2].n|p2);
planes[3].d = -(planes[3].n|p3);
planes[4].d = -(planes[4].n|p4);
planes[5].d = -(planes[5].n|p5);
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Computes the aabb points.
* \param pts [out] 8 box points
* \return true if success
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool AABB::ComputePoints(Point* pts) const
{
// Checkings
if(!pts) return false;
// Get box corners
Point min; GetMin(min);
Point max; GetMax(max);
// 7+------+6 0 = ---
// /| /| 1 = +--
// / | / | 2 = ++-
// / 4+---/--+5 3 = -+-
// 3+------+2 / y z 4 = --+
// | / | / | / 5 = +-+
// |/ |/ |/ 6 = +++
// 0+------+1 *---x 7 = -++
// Generate 8 corners of the bbox
pts[0] = Point(min.x, min.y, min.z);
pts[1] = Point(max.x, min.y, min.z);
pts[2] = Point(max.x, max.y, min.z);
pts[3] = Point(min.x, max.y, min.z);
pts[4] = Point(min.x, min.y, max.z);
pts[5] = Point(max.x, min.y, max.z);
pts[6] = Point(max.x, max.y, max.z);
pts[7] = Point(min.x, max.y, max.z);
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Gets vertex normals.
* \param pts [out] 8 box points
* \return true if success
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
const Point* AABB::GetVertexNormals() const
{
static float VertexNormals[] =
{
-INVSQRT3, -INVSQRT3, -INVSQRT3,
INVSQRT3, -INVSQRT3, -INVSQRT3,
INVSQRT3, INVSQRT3, -INVSQRT3,
-INVSQRT3, INVSQRT3, -INVSQRT3,
-INVSQRT3, -INVSQRT3, INVSQRT3,
INVSQRT3, -INVSQRT3, INVSQRT3,
INVSQRT3, INVSQRT3, INVSQRT3,
-INVSQRT3, INVSQRT3, INVSQRT3
};
return (const Point*)VertexNormals;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Returns edges.
* \return 24 indices (12 edges) indexing the list returned by ComputePoints()
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
const udword* AABB::GetEdges() const
{
static udword Indices[] = {
0, 1, 1, 2, 2, 3, 3, 0,
7, 6, 6, 5, 5, 4, 4, 7,
1, 5, 6, 2,
3, 7, 4, 0
};
return Indices;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Returns edge normals.
* \return edge normals in local space
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
const Point* AABB::GetEdgeNormals() const
{
static float EdgeNormals[] =
{
0, -INVSQRT2, -INVSQRT2, // 0-1
INVSQRT2, 0, -INVSQRT2, // 1-2
0, INVSQRT2, -INVSQRT2, // 2-3
-INVSQRT2, 0, -INVSQRT2, // 3-0
0, INVSQRT2, INVSQRT2, // 7-6
INVSQRT2, 0, INVSQRT2, // 6-5
0, -INVSQRT2, INVSQRT2, // 5-4
-INVSQRT2, 0, INVSQRT2, // 4-7
INVSQRT2, -INVSQRT2, 0, // 1-5
INVSQRT2, INVSQRT2, 0, // 6-2
-INVSQRT2, INVSQRT2, 0, // 3-7
-INVSQRT2, -INVSQRT2, 0 // 4-0
};
return (const Point*)EdgeNormals;
}
// ===========================================================================
// (C) 1996-98 Vienna University of Technology
// ===========================================================================
// NAME: bboxarea
// TYPE: c++ code
// PROJECT: Bounding Box Area
// CONTENT: Computes area of 2D projection of 3D oriented bounding box
// VERSION: 1.0
// ===========================================================================
// AUTHORS: ds Dieter Schmalstieg
// ep Erik Pojar
// ===========================================================================
// HISTORY:
//
// 19-sep-99 15:23:03 ds last modification
// 01-dec-98 15:23:03 ep created
// ===========================================================================
//----------------------------------------------------------------------------
// SAMPLE CODE STARTS HERE
//----------------------------------------------------------------------------
// NOTE: This sample program requires OPEN INVENTOR!
//indexlist: this table stores the 64 possible cases of classification of
//the eyepoint with respect to the 6 defining planes of the bbox (2^6=64)
//only 26 (3^3-1, where 1 is "inside" cube) of these cases are valid.
//the first 6 numbers in each row are the indices of the bbox vertices that
//form the outline of which we want to compute the area (counterclockwise
//ordering), the 7th entry means the number of vertices in the outline.
//there are 6 cases with a single face and and a 4-vertex outline, and
//20 cases with 2 or 3 faces and a 6-vertex outline. a value of 0 indicates
//an invalid case.
// Original list was made of 7 items, I added an 8th element:
// - to padd on a cache line
// - to repeat the first entry to avoid modulos
//
// I also replaced original ints with sbytes.
static const sbyte gIndexList[64][8] =
{
{-1,-1,-1,-1,-1,-1,-1, 0}, // 0 inside
{ 0, 4, 7, 3, 0,-1,-1, 4}, // 1 left
{ 1, 2, 6, 5, 1,-1,-1, 4}, // 2 right
{-1,-1,-1,-1,-1,-1,-1, 0}, // 3 -
{ 0, 1, 5, 4, 0,-1,-1, 4}, // 4 bottom
{ 0, 1, 5, 4, 7, 3, 0, 6}, // 5 bottom, left
{ 0, 1, 2, 6, 5, 4, 0, 6}, // 6 bottom, right
{-1,-1,-1,-1,-1,-1,-1, 0}, // 7 -
{ 2, 3, 7, 6, 2,-1,-1, 4}, // 8 top
{ 0, 4, 7, 6, 2, 3, 0, 6}, // 9 top, left
{ 1, 2, 3, 7, 6, 5, 1, 6}, //10 top, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //11 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //12 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //13 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //14 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //15 -
{ 0, 3, 2, 1, 0,-1,-1, 4}, //16 front
{ 0, 4, 7, 3, 2, 1, 0, 6}, //17 front, left
{ 0, 3, 2, 6, 5, 1, 0, 6}, //18 front, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //19 -
{ 0, 3, 2, 1, 5, 4, 0, 6}, //20 front, bottom
{ 1, 5, 4, 7, 3, 2, 1, 6}, //21 front, bottom, left
{ 0, 3, 2, 6, 5, 4, 0, 6}, //22 front, bottom, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //23 -
{ 0, 3, 7, 6, 2, 1, 0, 6}, //24 front, top
{ 0, 4, 7, 6, 2, 1, 0, 6}, //25 front, top, left
{ 0, 3, 7, 6, 5, 1, 0, 6}, //26 front, top, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //27 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //28 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //29 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //30 -
{-1,-1,-1,-1,-1,-1,-1, 0}, //31 -
{ 4, 5, 6, 7, 4,-1,-1, 4}, //32 back
{ 0, 4, 5, 6, 7, 3, 0, 6}, //33 back, left
{ 1, 2, 6, 7, 4, 5, 1, 6}, //34 back, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //35 -
{ 0, 1, 5, 6, 7, 4, 0, 6}, //36 back, bottom
{ 0, 1, 5, 6, 7, 3, 0, 6}, //37 back, bottom, left
{ 0, 1, 2, 6, 7, 4, 0, 6}, //38 back, bottom, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //39 -
{ 2, 3, 7, 4, 5, 6, 2, 6}, //40 back, top
{ 0, 4, 5, 6, 2, 3, 0, 6}, //41 back, top, left
{ 1, 2, 3, 7, 4, 5, 1, 6}, //42 back, top, right
{-1,-1,-1,-1,-1,-1,-1, 0}, //43 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //44 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //45 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //46 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //47 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //48 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //49 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //50 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //51 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //52 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //53 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //54 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //55 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //56 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //57 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //58 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //59 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //60 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //61 invalid
{-1,-1,-1,-1,-1,-1,-1, 0}, //62 invalid
{-1,-1,-1,-1,-1,-1,-1, 0} //63 invalid
};
const sbyte* AABB::ComputeOutline(const Point& local_eye, sdword& num) const
{
// Get box corners
Point min; GetMin(min);
Point max; GetMax(max);
// Compute 6-bit code to classify eye with respect to the 6 defining planes of the bbox
int pos = ((local_eye.x < min.x) ? 1 : 0) // 1 = left
+ ((local_eye.x > max.x) ? 2 : 0) // 2 = right
+ ((local_eye.y < min.y) ? 4 : 0) // 4 = bottom
+ ((local_eye.y > max.y) ? 8 : 0) // 8 = top
+ ((local_eye.z < min.z) ? 16 : 0) // 16 = front
+ ((local_eye.z > max.z) ? 32 : 0); // 32 = back
// Look up number of vertices in outline
num = (sdword)gIndexList[pos][7];
// Zero indicates invalid case
if(!num) return null;
return &gIndexList[pos][0];
}
// calculateBoxArea: computes the screen-projected 2D area of an oriented 3D bounding box
//const Point& eye, //eye point (in bbox object coordinates)
//const AABB& box, //3d bbox
//const Matrix4x4& mat, //free transformation for bbox
//float width, float height, int& num)
float AABB::ComputeBoxArea(const Point& eye, const Matrix4x4& mat, float width, float height, sdword& num) const
{
const sbyte* Outline = ComputeOutline(eye, num);
if(!Outline) return -1.0f;
// Compute box vertices
Point vertexBox[8], dst[8];
ComputePoints(vertexBox);
// Transform all outline corners into 2D screen space
for(sdword i=0;i<num;i++)
{
HPoint Projected;
vertexBox[Outline[i]].ProjectToScreen(width, height, mat, Projected);
dst[i] = Projected;
}
float Sum = (dst[num-1][0] - dst[0][0]) * (dst[num-1][1] + dst[0][1]);
for(int i=0; i<num-1; i++)
Sum += (dst[i][0] - dst[i+1][0]) * (dst[i][1] + dst[i+1][1]);
return Sum * 0.5f; //return computed value corrected by 0.5
}
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