Transform Struct Reference

representation d'une transformation, une matrice 4x4, organisee par ligne / row major. More...

#include <mat.h>

Public Member Functions
	Transform (const float t00=1, const float t01=0, const float t02=0, const float t03=0, const float t10=0, const float t11=1, const float t12=0, const float t13=0, const float t20=0, const float t21=0, const float t22=1, const float t23=0, const float t30=0, const float t31=0, const float t32=0, const float t33=1)
	constructeur.
	Transform (const Vector &x, const Vector &y, const Vector &z, const Vector &w)
	constructeur a partir de 4 Vector colonnes, met (0, 0, 0, 1) dans la 4e ligne
Transform &	column (const int id, const float t0, const float t1, const float t2, const float t3)
	initialise une colonne de la matrice a partir de 4 floats.
Transform &	row (const int id, const float t0, const float t1, const float t2, const float t3)
	initialise une ligne de la matrice.
Transform &	column_major (const float matrix[16])
	initialise la matrice avec 16 floats organises par colonne.
Transform &	row_major (const float matrix[16])
	initialise la matrice avec 16 floats organises par ligne.
Vector	operator[] (const int c) const
	renvoie le Vector colonne c de la matrice
Point	operator() (const Point &p) const
	renvoie le point transforme.
Vector	operator() (const Vector &v) const
	renvoie le vecteur transforme.
vec4	operator() (const vec4 &v) const
	renvoie le point/vecteur homogene transforme.
Transform	operator() (const Transform &b) const
	renvoie la composition de la transformation this et b, t = this * b. permet de transformer un point sans "ambiguite" Point q= a(b(c(p)));
Transform	transpose () const
	renvoie la transposee de la matrice.
Transform	inverse () const
	renvoie l'inverse de la matrice.
Transform	normal () const
	renvoie la transformation a appliquer aux normales d'un objet transforme par la matrice m.
const float *	data () const
	renvoie l'adresse de la premiere valeur de la matrice.

Public Attributes
float	m [4][4]

Detailed Description

representation d'une transformation, une matrice 4x4, organisee par ligne / row major.

Definition at line 20 of file mat.h.

Constructor & Destructor Documentation

Transform() [1/2]

Transform::Transform	(	const float	t00 = 1,
		const float	t01 = 0,
		const float	t02 = 0,
		const float	t03 = 0,
		const float	t10 = 0,
		const float	t11 = 1,
		const float	t12 = 0,
		const float	t13 = 0,
		const float	t20 = 0,
		const float	t21 = 0,
		const float	t22 = 1,
		const float	t23 = 0,
		const float	t30 = 0,
		const float	t31 = 0,
		const float	t32 = 0,
		const float	t33 = 1
	)

constructeur.

Definition at line 20 of file mat.cpp.

{
    m[0][0]= t00; m[0][1]= t01; m[0][2]= t02; m[0][3]= t03;
    m[1][0]= t10; m[1][1]= t11; m[1][2]= t12; m[1][3]= t13;
    m[2][0]= t20; m[2][1]= t21; m[2][2]= t22; m[2][3]= t23;
    m[3][0]= t30; m[3][1]= t31; m[3][2]= t32; m[3][3]= t33;
}

Transform() [2/2]

Transform::Transform	(	const Vector &	x,
		const Vector &	y,
		const Vector &	z,
		const Vector &	w
	)

constructeur a partir de 4 Vector colonnes, met (0, 0, 0, 1) dans la 4e ligne

Definition at line 64 of file mat.cpp.

{
    m[0][0] = x.x;  m[0][1] = y.x;  m[0][2] = z.x;  m[0][3] = w.x;
    m[1][0] = x.y;  m[1][1] = y.y;  m[1][2] = z.y;  m[1][3] = w.y;
    m[2][0] = x.z;  m[2][1] = y.z;  m[2][2] = z.z;  m[2][3] = w.z;
    m[3][0] = 0;    m[3][1] = 0;    m[3][2] = 0;    m[3][3] = 1;
}

Member Function Documentation

column()

Transform & Transform::column	(	const int	id,
		const float	t0,
		const float	t1,
		const float	t2,
		const float	t3
	)

initialise une colonne de la matrice a partir de 4 floats.

Definition at line 32 of file mat.cpp.

{
    m[0][id]= t0;
    m[1][id]= t1;
    m[2][id]= t2;
    m[3][id]= t3;
    return *this;
}

row()

Transform & Transform::row	(	const int	id,
		const float	t0,
		const float	t1,
		const float	t2,
		const float	t3
	)

initialise une ligne de la matrice.

Definition at line 41 of file mat.cpp.

{
    m[id][0]= t0;
    m[id][1]= t1;
    m[id][2]= t2;
    m[id][3]= t3;
    return *this;
}

column_major()

Transform & Transform::column_major

(

const float

matrix[16]

)

initialise la matrice avec 16 floats organises par colonne.

Definition at line 50 of file mat.cpp.

{
    for(int i= 0; i < 4; i++)
        column(i, matrix[4*i], matrix[4*i+1], matrix[4*i+2], matrix[4*i+3]);
    return *this;
}

row_major()

Transform & Transform::row_major

(

const float

matrix[16]

)

initialise la matrice avec 16 floats organises par ligne.

Definition at line 57 of file mat.cpp.

{
    for(int i= 0; i < 4; i++)
        row(i, matrix[4*i], matrix[4*i+1], matrix[4*i+2], matrix[4*i+3]);
    return *this;
}

operator[]()

Vector Transform::operator[]

(

const int

c

)

const

renvoie le Vector colonne c de la matrice

Definition at line 72 of file mat.cpp.

{
    assert(c >= 0 && c <= 3);
    return Vector(m[0][c], m[1][c], m[2][c]);
}

operator()() [1/4]

Point Transform::operator()

(

const Point &

p

)

const

renvoie le point transforme.

Definition at line 80 of file mat.cpp.

{
    float x= p.x;
    float y= p.y;
    float z= p.z;
 
    float xt= m[0][0] * x + m[0][1] * y + m[0][2] * z + m[0][3];        // dot(vec4(m[0]), vec4(p, 1))
    float yt= m[1][0] * x + m[1][1] * y + m[1][2] * z + m[1][3];        // dot(vec4(m[1]), vec4(p, 1))
    float zt= m[2][0] * x + m[2][1] * y + m[2][2] * z + m[2][3];        // dot(vec4(m[2]), vec4(p, 1))
    float wt= m[3][0] * x + m[3][1] * y + m[3][2] * z + m[3][3];        // dot(vec4(m[3]), vec4(p, 1))
 
    assert(wt != 0);
    float w= 1.f / wt;
    if(wt == 1.f)
        return Point(xt, yt, zt);
    else
        return Point(xt*w, yt*w, zt*w);
}

operator()() [2/4]

Vector Transform::operator()

(

const Vector &

v

)

const

renvoie le vecteur transforme.

Definition at line 100 of file mat.cpp.

{
    float x= v.x;
    float y= v.y;
    float z= v.z;
 
    float xt= m[0][0] * x + m[0][1] * y + m[0][2] * z;                  // dot(vec4(m[0]), vec4(v, 0))
    float yt= m[1][0] * x + m[1][1] * y + m[1][2] * z;                  // dot(vec4(m[1]), vec4(v, 0))
    float zt= m[2][0] * x + m[2][1] * y + m[2][2] * z;                  // dot(vec4(m[2]), vec4(v, 0))
    // dot(vec4(m[3]), vec4(v, 0)) == dot(vec4(0, 0, 0, 1), vec4(v, 0)) == 0 par definition
 
    return Vector(xt, yt, zt);
}

operator()() [3/4]

vec4 Transform::operator()

(

const vec4 &

v

)

const

renvoie le point/vecteur homogene transforme.

Definition at line 115 of file mat.cpp.

{
    float x= v.x;
    float y= v.y;
    float z= v.z;
    float w= v.w;
 
    float xt= m[0][0] * x + m[0][1] * y + m[0][2] * z + m[0][3] * w;    // dot(vec4(m[0]), v)
    float yt= m[1][0] * x + m[1][1] * y + m[1][2] * z + m[1][3] * w;    // dot(vec4(m[1]), v)
    float zt= m[2][0] * x + m[2][1] * y + m[2][2] * z + m[2][3] * w;    // dot(vec4(m[2]), v)
    float wt= m[3][0] * x + m[3][1] * y + m[3][2] * z + m[3][3] * w;    // dot(vec4(m[3]), v)
 
    return vec4(xt, yt, zt, wt);
}

operator()() [4/4]

Transform Transform::operator()

(

const Transform &

b

)

const

renvoie la composition de la transformation this et b, t = this * b. permet de transformer un point sans "ambiguite" Point q= a(b(c(p)));

Definition at line 141 of file mat.cpp.

{
    return compose_transform(*this, b);
}

transpose()

Transform Transform::transpose

(

)

const

renvoie la transposee de la matrice.

Definition at line 131 of file mat.cpp.

{
    return Transform(
        m[0][0], m[1][0], m[2][0], m[3][0],
        m[0][1], m[1][1], m[2][1], m[3][1],
        m[0][2], m[1][2], m[2][2], m[3][2],
        m[0][3], m[1][3], m[2][3], m[3][3]);
}

inverse()

Transform Transform::inverse

(

)

const

renvoie l'inverse de la matrice.

Definition at line 365 of file mat.cpp.

{
    Transform minv= *this;
 
    int indxc[4], indxr[4];
    int ipiv[4] = { 0, 0, 0, 0 };
 
    for (int i = 0; i < 4; i++) {
        int irow = -1, icol = -1;
        float big = 0.f;
 
        // Choose pivot
        for (int j = 0; j < 4; j++) {
            if (ipiv[j] != 1) {
                for (int k = 0; k < 4; k++) {
                    if (ipiv[k] == 0) {
                        if (fabsf(minv.m[j][k]) >= big) {
                            big = std::abs(minv.m[j][k]);
                            irow = j;
                            icol = k;
                        }
                    }
                    else if (ipiv[k] > 1)
                        printf("singular matrix in Transform::inverse()\n");
                }
            }
        }
 
        assert(irow >= 0 && irow < 4);
        assert(icol >= 0 && icol < 4);
 
        ++ipiv[icol];
        // Swap rows _irow_ and _icol_ for pivot
        if (irow != icol) {
            for (int k = 0; k < 4; ++k)
                std::swap(minv.m[irow][k], minv.m[icol][k]);
        }
 
        indxr[i] = irow;
        indxc[i] = icol;
        if (minv.m[icol][icol] == 0.)
            printf("singular matrix in Transform::inverse()\n");
 
        // Set $m[icol][icol]$ to one by scaling row _icol_ appropriately
        float pivinv = 1.f / minv.m[icol][icol];
        minv.m[icol][icol] = 1.f;
        for (int j = 0; j < 4; j++)
            minv.m[icol][j] *= pivinv;
 
        // Subtract this row from others to zero out their columns
        for (int j = 0; j < 4; j++) {
            if (j != icol) {
                float save = minv.m[j][icol];
                minv.m[j][icol] = 0;
                for (int k = 0; k < 4; k++)
                    minv.m[j][k] -= minv.m[icol][k]*save;
            }
        }
    }
 
    // Swap columns to reflect permutation
    for (int j = 3; j >= 0; j--) {
        if (indxr[j] != indxc[j]) {
            for (int k = 0; k < 4; k++)
                std::swap(minv.m[k][indxr[j]], minv.m[k][indxc[j]]);
        }
    }
 
    return minv;
}

normal()

Transform Transform::normal

(

)

const

renvoie la transformation a appliquer aux normales d'un objet transforme par la matrice m.

Definition at line 147 of file mat.cpp.

{
    return inverse().transpose();
}

data()

const float * Transform::data ( ) const

inline

renvoie l'adresse de la premiere valeur de la matrice.

Definition at line 65 of file mat.h.

{ return &m[0][0]; }

Member Data Documentation

m

float Transform::m[4][4]

Definition at line 67 of file mat.h.

---

The documentation for this struct was generated from the following files:

• src/mat.h
• src/mat.cpp