///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Contains code for 3D vectors.
* \file IcePoint.h
* \author Pierre Terdiman
* \date April, 4, 2000
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Include Guard
#ifndef __ICEPOINT_H__
#define __ICEPOINT_H__
// Forward declarations
class HPoint;
class Plane;
class Matrix3x3;
class Matrix4x4;
#define CROSS2D(a, b) (a.x*b.y - b.x*a.y)
const float EPSILON2 = 1.0e-20f;
class ICEMATHS_API Point
{
public:
//! Empty constructor
inline_ Point() {}
//! Constructor from a single float
// inline_ Point(float val) : x(val), y(val), z(val) {}
// Removed since it introduced the nasty "Point T = *Matrix4x4.GetTrans();" bug.......
//! Constructor from floats
inline_ Point(float xx, float yy, float zz) : x(xx), y(yy), z(zz) {}
//! Constructor from array
inline_ Point(const float f[3]) : x(f[X]), y(f[Y]), z(f[Z]) {}
//! Copy constructor
inline_ Point(const Point& p) : x(p.x), y(p.y), z(p.z) {}
//! Destructor
inline_ ~Point() {}
//! Clears the vector
inline_ Point& Zero() { x = y = z = 0.0f; return *this; }
//! + infinity
inline_ Point& SetPlusInfinity() { x = y = z = MAX_FLOAT; return *this; }
//! - infinity
inline_ Point& SetMinusInfinity() { x = y = z = MIN_FLOAT; return *this; }
//! Sets positive unit random vector
Point& PositiveUnitRandomVector();
//! Sets unit random vector
Point& UnitRandomVector();
//! Assignment from values
inline_ Point& Set(float xx, float yy, float zz) { x = xx; y = yy; z = zz; return *this; }
//! Assignment from array
inline_ Point& Set(const float f[3]) { x = f[X]; y = f[Y]; z = f[Z]; return *this; }
//! Assignment from another point
inline_ Point& Set(const Point& src) { x = src.x; y = src.y; z = src.z; return *this; }
//! Adds a vector
inline_ Point& Add(const Point& p) { x += p.x; y += p.y; z += p.z; return *this; }
//! Adds a vector
inline_ Point& Add(float xx, float yy, float zz) { x += xx; y += yy; z += zz; return *this; }
//! Adds a vector
inline_ Point& Add(const float f[3]) { x += f[X]; y += f[Y]; z += f[Z]; return *this; }
//! Adds vectors
inline_ Point& Add(const Point& p, const Point& q) { x = p.x+q.x; y = p.y+q.y; z = p.z+q.z; return *this; }
//! Subtracts a vector
inline_ Point& Sub(const Point& p) { x -= p.x; y -= p.y; z -= p.z; return *this; }
//! Subtracts a vector
inline_ Point& Sub(float xx, float yy, float zz) { x -= xx; y -= yy; z -= zz; return *this; }
//! Subtracts a vector
inline_ Point& Sub(const float f[3]) { x -= f[X]; y -= f[Y]; z -= f[Z]; return *this; }
//! Subtracts vectors
inline_ Point& Sub(const Point& p, const Point& q) { x = p.x-q.x; y = p.y-q.y; z = p.z-q.z; return *this; }
//! this = -this
inline_ Point& Neg() { x = -x; y = -y; z = -z; return *this; }
//! this = -a
inline_ Point& Neg(const Point& a) { x = -a.x; y = -a.y; z = -a.z; return *this; }
//! Multiplies by a scalar
inline_ Point& Mult(float s) { x *= s; y *= s; z *= s; return *this; }
//! this = a * scalar
inline_ Point& Mult(const Point& a, float scalar)
{
x = a.x * scalar;
y = a.y * scalar;
z = a.z * scalar;
return *this;
}
//! this = a + b * scalar
inline_ Point& Mac(const Point& a, const Point& b, float scalar)
{
x = a.x + b.x * scalar;
y = a.y + b.y * scalar;
z = a.z + b.z * scalar;
return *this;
}
//! this = this + a * scalar
inline_ Point& Mac(const Point& a, float scalar)
{
x += a.x * scalar;
y += a.y * scalar;
z += a.z * scalar;
return *this;
}
//! this = a - b * scalar
inline_ Point& Msc(const Point& a, const Point& b, float scalar)
{
x = a.x - b.x * scalar;
y = a.y - b.y * scalar;
z = a.z - b.z * scalar;
return *this;
}
//! this = this - a * scalar
inline_ Point& Msc(const Point& a, float scalar)
{
x -= a.x * scalar;
y -= a.y * scalar;
z -= a.z * scalar;
return *this;
}
//! this = a + b * scalarb + c * scalarc
inline_ Point& Mac2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
{
x = a.x + b.x * scalarb + c.x * scalarc;
y = a.y + b.y * scalarb + c.y * scalarc;
z = a.z + b.z * scalarb + c.z * scalarc;
return *this;
}
//! this = a - b * scalarb - c * scalarc
inline_ Point& Msc2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
{
x = a.x - b.x * scalarb - c.x * scalarc;
y = a.y - b.y * scalarb - c.y * scalarc;
z = a.z - b.z * scalarb - c.z * scalarc;
return *this;
}
//! this = mat * a
inline_ Point& Mult(const Matrix3x3& mat, const Point& a);
//! this = mat1 * a1 + mat2 * a2
inline_ Point& Mult2(const Matrix3x3& mat1, const Point& a1, const Matrix3x3& mat2, const Point& a2);
//! this = this + mat * a
inline_ Point& Mac(const Matrix3x3& mat, const Point& a);
//! this = transpose(mat) * a
inline_ Point& TransMult(const Matrix3x3& mat, const Point& a);
//! Linear interpolate between two vectors: this = a + t * (b - a)
inline_ Point& Lerp(const Point& a, const Point& b, float t)
{
x = a.x + t * (b.x - a.x);
y = a.y + t * (b.y - a.y);
z = a.z + t * (b.z - a.z);
return *this;
}
//! Hermite interpolate between p1 and p2. p0 and p3 are used for finding gradient at p1 and p2.
//! this = p0 * (2t^2 - t^3 - t)/2
//! + p1 * (3t^3 - 5t^2 + 2)/2
//! + p2 * (4t^2 - 3t^3 + t)/2
//! + p3 * (t^3 - t^2)/2
inline_ Point& Herp(const Point& p0, const Point& p1, const Point& p2, const Point& p3, float t)
{
float t2 = t * t;
float t3 = t2 * t;
float kp0 = (2.0f * t2 - t3 - t) * 0.5f;
float kp1 = (3.0f * t3 - 5.0f * t2 + 2.0f) * 0.5f;
float kp2 = (4.0f * t2 - 3.0f * t3 + t) * 0.5f;
float kp3 = (t3 - t2) * 0.5f;
x = p0.x * kp0 + p1.x * kp1 + p2.x * kp2 + p3.x * kp3;
y = p0.y * kp0 + p1.y * kp1 + p2.y * kp2 + p3.y * kp3;
z = p0.z * kp0 + p1.z * kp1 + p2.z * kp2 + p3.z * kp3;
return *this;
}
//! this = rotpos * r + linpos
inline_ Point& Transform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
//! this = trans(rotpos) * (r - linpos)
inline_ Point& InvTransform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
//! Returns MIN(x, y, z);
inline_ float Min() const { return MIN(x, MIN(y, z)); }
//! Returns MAX(x, y, z);
inline_ float Max() const { return MAX(x, MAX(y, z)); }
//! Sets each element to be componentwise minimum
inline_ Point& Min(const Point& p) { x = MIN(x, p.x); y = MIN(y, p.y); z = MIN(z, p.z); return *this; }
//! Sets each element to be componentwise maximum
inline_ Point& Max(const Point& p) { x = MAX(x, p.x); y = MAX(y, p.y); z = MAX(z, p.z); return *this; }
//! Clamps each element
inline_ Point& Clamp(float min, float max)
{
if(x<min) x=min; if(x>max) x=max;
if(y<min) y=min; if(y>max) y=max;
if(z<min) z=min; if(z>max) z=max;
return *this;
}
//! Computes square magnitude
inline_ float SquareMagnitude() const { return x*x + y*y + z*z; }
//! Computes magnitude
inline_ float Magnitude() const { return sqrtf(x*x + y*y + z*z); }
//! Computes volume
inline_ float Volume() const { return x * y * z; }
//! Checks the point is near zero
inline_ bool ApproxZero() const { return SquareMagnitude() < EPSILON2; }
//! Tests for exact zero vector
inline_ BOOL IsZero() const
{
if(IR(x) || IR(y) || IR(z)) return FALSE;
return TRUE;
}
//! Checks point validity
inline_ BOOL IsValid() const
{
if(!IsValidFloat(x)) return FALSE;
if(!IsValidFloat(y)) return FALSE;
if(!IsValidFloat(z)) return FALSE;
return TRUE;
}
//! Slighty moves the point
void Tweak(udword coord_mask, udword tweak_mask)
{
if(coord_mask&1) { udword Dummy = IR(x); Dummy^=tweak_mask; x = FR(Dummy); }
if(coord_mask&2) { udword Dummy = IR(y); Dummy^=tweak_mask; y = FR(Dummy); }
if(coord_mask&4) { udword Dummy = IR(z); Dummy^=tweak_mask; z = FR(Dummy); }
}
#define TWEAKMASK 0x3fffff
#define TWEAKNOTMASK ~TWEAKMASK
//! Slighty moves the point out
inline_ void TweakBigger()
{
udword Dummy = (IR(x)&TWEAKNOTMASK); if(!IS_NEGATIVE_FLOAT(x)) Dummy+=TWEAKMASK+1; x = FR(Dummy);
Dummy = (IR(y)&TWEAKNOTMASK); if(!IS_NEGATIVE_FLOAT(y)) Dummy+=TWEAKMASK+1; y = FR(Dummy);
Dummy = (IR(z)&TWEAKNOTMASK); if(!IS_NEGATIVE_FLOAT(z)) Dummy+=TWEAKMASK+1; z = FR(Dummy);
}
//! Slighty moves the point in
inline_ void TweakSmaller()
{
udword Dummy = (IR(x)&TWEAKNOTMASK); if(IS_NEGATIVE_FLOAT(x)) Dummy+=TWEAKMASK+1; x = FR(Dummy);
Dummy = (IR(y)&TWEAKNOTMASK); if(IS_NEGATIVE_FLOAT(y)) Dummy+=TWEAKMASK+1; y = FR(Dummy);
Dummy = (IR(z)&TWEAKNOTMASK); if(IS_NEGATIVE_FLOAT(z)) Dummy+=TWEAKMASK+1; z = FR(Dummy);
}
//! Normalizes the vector
inline_ Point& Normalize()
{
float M = x*x + y*y + z*z;
if(M)
{
M = 1.0f / sqrtf(M);
x *= M;
y *= M;
z *= M;
}
return *this;
}
//! Sets vector length
inline_ Point& SetLength(float length)
{
float NewLength = length / Magnitude();
x *= NewLength;
y *= NewLength;
z *= NewLength;
return *this;
}
//! Clamps vector length
inline_ Point& ClampLength(float limit_length)
{
if(limit_length>=0.0f) // Magnitude must be positive
{
float CurrentSquareLength = SquareMagnitude();
if(CurrentSquareLength > limit_length * limit_length)
{
float Coeff = limit_length / sqrtf(CurrentSquareLength);
x *= Coeff;
y *= Coeff;
z *= Coeff;
}
}
return *this;
}
//! Computes distance to another point
inline_ float Distance(const Point& b) const
{
return sqrtf((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
}
//! Computes square distance to another point
inline_ float SquareDistance(const Point& b) const
{
return ((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
}
//! Dot product dp = this|a
inline_ float Dot(const Point& p) const { return p.x * x + p.y * y + p.z * z; }
//! Cross product this = a x b
inline_ Point& Cross(const Point& a, const Point& b)
{
x = a.y * b.z - a.z * b.y;
y = a.z * b.x - a.x * b.z;
z = a.x * b.y - a.y * b.x;
return *this;
}
//! Vector code ( bitmask = sign(z) | sign(y) | sign(x) )
inline_ udword VectorCode() const
{
return (IR(x)>>31) | ((IR(y)&SIGN_BITMASK)>>30) | ((IR(z)&SIGN_BITMASK)>>29);
}
//! Returns largest axis
inline_ PointComponent LargestAxis() const
{
const float* Vals = &x;
PointComponent m = X;
if(Vals[Y] > Vals[m]) m = Y;
if(Vals[Z] > Vals[m]) m = Z;
return m;
}
//! Returns closest axis
inline_ PointComponent ClosestAxis() const
{
const float* Vals = &x;
PointComponent m = X;
if(AIR(Vals[Y]) > AIR(Vals[m])) m = Y;
if(AIR(Vals[Z]) > AIR(Vals[m])) m = Z;
return m;
}
//! Returns smallest axis
inline_ PointComponent SmallestAxis() const
{
const float* Vals = &x;
PointComponent m = X;
if(Vals[Y] < Vals[m]) m = Y;
if(Vals[Z] < Vals[m]) m = Z;
return m;
}
//! Refracts the point
Point& Refract(const Point& eye, const Point& n, float refractindex, Point& refracted);
//! Projects the point onto a plane
Point& ProjectToPlane(const Plane& p);
//! Projects the point onto the screen
void ProjectToScreen(float halfrenderwidth, float halfrenderheight, const Matrix4x4& mat, HPoint& projected) const;
//! Unfolds the point onto a plane according to edge(a,b)
Point& Unfold(Plane& p, Point& a, Point& b);
//! Hash function from Ville Miettinen
inline_ udword GetHashValue() const
{
const udword* h = (const udword*)(this);
udword f = (h[0]+h[1]*11-(h[2]*17)) & 0x7fffffff; // avoid problems with +-0
return (f>>22)^(f>>12)^(f);
}
//! Stuff magic values in the point, marking it as explicitely not used.
void SetNotUsed();
//! Checks the point is marked as not used
BOOL IsNotUsed() const;
// Arithmetic operators
//! Unary operator for Point Negate = - Point
inline_ Point operator-() const { return Point(-x, -y, -z); }
//! Operator for Point Plus = Point + Point.
inline_ Point operator+(const Point& p) const { return Point(x + p.x, y + p.y, z + p.z); }
//! Operator for Point Minus = Point - Point.
inline_ Point operator-(const Point& p) const { return Point(x - p.x, y - p.y, z - p.z); }
//! Operator for Point Mul = Point * Point.
inline_ Point operator*(const Point& p) const { return Point(x * p.x, y * p.y, z * p.z); }
//! Operator for Point Scale = Point * float.
inline_ Point operator*(float s) const { return Point(x * s, y * s, z * s ); }
//! Operator for Point Scale = float * Point.
inline_ friend Point operator*(float s, const Point& p) { return Point(s * p.x, s * p.y, s * p.z); }
//! Operator for Point Div = Point / Point.
inline_ Point operator/(const Point& p) const { return Point(x / p.x, y / p.y, z / p.z); }
//! Operator for Point Scale = Point / float.
inline_ Point operator/(float s) const { s = 1.0f / s; return Point(x * s, y * s, z * s); }
//! Operator for Point Scale = float / Point.
inline_ friend Point operator/(float s, const Point& p) { return Point(s / p.x, s / p.y, s / p.z); }
//! Operator for float DotProd = Point | Point.
inline_ float operator|(const Point& p) const { return x*p.x + y*p.y + z*p.z; }
//! Operator for Point VecProd = Point ^ Point.
inline_ Point operator^(const Point& p) const
{
return Point(
y * p.z - z * p.y,
z * p.x - x * p.z,
x * p.y - y * p.x );
}
//! Operator for Point += Point.
inline_ Point& operator+=(const Point& p) { x += p.x; y += p.y; z += p.z; return *this; }
//! Operator for Point += float.
inline_ Point& operator+=(float s) { x += s; y += s; z += s; return *this; }
//! Operator for Point -= Point.
inline_ Point& operator-=(const Point& p) { x -= p.x; y -= p.y; z -= p.z; return *this; }
//! Operator for Point -= float.
inline_ Point& operator-=(float s) { x -= s; y -= s; z -= s; return *this; }
//! Operator for Point *= Point.
inline_ Point& operator*=(const Point& p) { x *= p.x; y *= p.y; z *= p.z; return *this; }
//! Operator for Point *= float.
inline_ Point& operator*=(float s) { x *= s; y *= s; z *= s; return *this; }
//! Operator for Point /= Point.
inline_ Point& operator/=(const Point& p) { x /= p.x; y /= p.y; z /= p.z; return *this; }
//! Operator for Point /= float.
inline_ Point& operator/=(float s) { s = 1.0f/s; x *= s; y *= s; z *= s; return *this; }
// Logical operators
//! Operator for "if(Point==Point)"
inline_ bool operator==(const Point& p) const { return ( (IR(x)==IR(p.x))&&(IR(y)==IR(p.y))&&(IR(z)==IR(p.z))); }
//! Operator for "if(Point!=Point)"
inline_ bool operator!=(const Point& p) const { return ( (IR(x)!=IR(p.x))||(IR(y)!=IR(p.y))||(IR(z)!=IR(p.z))); }
// Arithmetic operators
//! Operator for Point Mul = Point * Matrix3x3.
inline_ Point operator*(const Matrix3x3& mat) const
{
class ShadowMatrix3x3{ public: float m[3][3]; }; // To allow inlining
const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
return Point(
x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0],
x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1],
x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] );
}
//! Operator for Point Mul = Point * Matrix4x4.
inline_ Point operator*(const Matrix4x4& mat) const
{
class ShadowMatrix4x4{ public: float m[4][4]; }; // To allow inlining
const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
return Point(
x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0],
x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1],
x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2]);
}
//! Operator for Point *= Matrix3x3.
inline_ Point& operator*=(const Matrix3x3& mat)
{
class ShadowMatrix3x3{ public: float m[3][3]; }; // To allow inlining
const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0];
float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1];
float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2];
x = xp; y = yp; z = zp;
return *this;
}
//! Operator for Point *= Matrix4x4.
inline_ Point& operator*=(const Matrix4x4& mat)
{
class ShadowMatrix4x4{ public: float m[4][4]; }; // To allow inlining
const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0];
float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1];
float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2];
x = xp; y = yp; z = zp;
return *this;
}
// Cast operators
//! Cast a Point to a HPoint. w is set to zero.
operator HPoint() const;
inline_ operator const float*() const { return &x; }
inline_ operator float*() { return &x; }
public:
float x, y, z;
};
FUNCTION ICEMATHS_API void Normalize1(Point& a);
FUNCTION ICEMATHS_API void Normalize2(Point& a);
#endif //__ICEPOINT_H__
syntax highlighted by Code2HTML, v. 0.9.1