added method to get Projection matrix given near and far.

This commit is contained in:
Federico Ponchio 2012-08-29 13:21:22 +00:00
parent f16b821dc0
commit 0ac7034397
1 changed files with 257 additions and 219 deletions

View File

@ -141,106 +141,109 @@ template<class S>
class Camera
{
public:
typedef S ScalarType;
enum {
PERSPECTIVE = 0,
ORTHO = 1,
ISOMETRIC = 2,
CAVALIERI = 3
};
typedef S ScalarType;
enum {
PERSPECTIVE = 0,
ORTHO = 1,
ISOMETRIC = 2,
CAVALIERI = 3
};
Camera():
FocalMm(0.f),
ViewportPx(vcg::Point2<int>(0,0)),
PixelSizeMm(vcg::Point2<S>(0.0,0.0)),
CenterPx(vcg::Point2<S>(0.0,0.0)),
DistorCenterPx(vcg::Point2<S>(0.0,0.0)),
cameraType(0)
{
k[0] = k[1] = k[2] = k[3] = 0;
Camera():
FocalMm(0.f),
ViewportPx(vcg::Point2<int>(0,0)),
PixelSizeMm(vcg::Point2<S>(0.0,0.0)),
CenterPx(vcg::Point2<S>(0.0,0.0)),
DistorCenterPx(vcg::Point2<S>(0.0,0.0)),
cameraType(0)
{
k[0] = k[1] = k[2] = k[3] = 0;
}
//------ camera intrinsics
ScalarType FocalMm; /// Focal Distance: the distance between focal center and image plane. Expressed in mm
Point2<int> ViewportPx; /// Dimension of the Image Plane (in pixels)
Point2<S> PixelSizeMm; /// Dimension in mm of a single pixel
Point2<S> CenterPx; /// Position of the projection of the focal center on the image plane. Expressed in pixels
//------ camera intrinsics
ScalarType FocalMm; /// Focal Distance: the distance between focal center and image plane. Expressed in mm
Point2<int> ViewportPx; /// Dimension of the Image Plane (in pixels)
Point2<S> PixelSizeMm; /// Dimension in mm of a single pixel
Point2<S> CenterPx; /// Position of the projection of the focal center on the image plane. Expressed in pixels
Point2<S> DistorCenterPx; /// Position of the radial distortion center on the image plane in pixels
S k[4]; /// 1st & 2nd order radial lens distortion coefficient (only the first 2 terms are used)
//------------------------
Point2<S> DistorCenterPx; /// Position of the radial distortion center on the image plane in pixels
S k[4]; /// 1st & 2nd order radial lens distortion coefficient (only the first 2 terms are used)
//------------------------
int cameraType; /// Type of camera: PERSPECTIVE,ORTHO,ISOMETRIC,CAVALIERI
int cameraType; /// Type of camera: PERSPECTIVE,ORTHO,ISOMETRIC,CAVALIERI
void SetOrtho( S l,S r, S b, S t, vcg::Point2<int> viewport)
{
cameraType = ORTHO;
ViewportPx = viewport;
void SetOrtho( S l,S r, S b, S t, vcg::Point2<int> viewport)
{
cameraType = ORTHO;
ViewportPx = viewport;
PixelSizeMm[0] = (r-l) / (S)ViewportPx[0];
PixelSizeMm[1] = (t-b) / (S)ViewportPx[1];
PixelSizeMm[0] = (r-l) / (S)ViewportPx[0];
PixelSizeMm[1] = (t-b) / (S)ViewportPx[1];
CenterPx[0] = -l/(r-l) * (S)ViewportPx[0];
CenterPx[1] = -b/(t-b) * (S)ViewportPx[1];
CenterPx[0] = -l/(r-l) * (S)ViewportPx[0];
CenterPx[1] = -b/(t-b) * (S)ViewportPx[1];
};
};
bool IsOrtho() const
{
return ( cameraType == ORTHO );
}
bool IsOrtho() const
{
return ( cameraType == ORTHO );
}
//--- Set-up methods
//--- Set-up methods
/// set the camera specifying the perspecive view
inline void SetPerspective(S AngleDeg, S AspectRatio, S Focal, vcg::Point2<int> Viewport);
/// set the camera specifying the perspecive view
inline void SetPerspective(S AngleDeg, S AspectRatio, S Focal, vcg::Point2<int> Viewport);
/// set the camera specifying the cavalieri view
inline void SetCavalieri(S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport);
/// set the camera specifying the cavalieri view
inline void SetCavalieri(S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport);
/// set the camera specifying the isometric view
inline void SetIsometric(S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport);
/// set the camera specifying the isometric view
inline void SetIsometric(S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport);
/// set the camera specifying the frustum view
inline void SetFrustum(S dx, S sx, S bt, S tp, S Focal, vcg::Point2<int> Viewport);
//------------------
/// set the camera specifying the frustum view
inline void SetFrustum(S dx, S sx, S bt, S tp, S Focal, vcg::Point2<int> Viewport);
//------------------
/// returns the frustum
inline void GetFrustum(S & sx, S & dx, S & bt, S & tp, S & nr);
/// returns the projection matrix
vcg::Matrix44<S> GetMatrix(S nearVal, S farVal);
//--- Space transformation methods
/// returns the frustum
inline void GetFrustum(S & sx, S & dx, S & bt, S & tp, S & nr);
/// project a point from 3d CAMERA space to the camera local plane
inline vcg::Point2<S> Project(const vcg::Point3<S> & p) const;
//--- Space transformation methods
/// unproject a point from the camera local plane (plus depth) to 3d CAMERA space
inline vcg::Point3<S> UnProject(const vcg::Point2<S> & p, const S & d) const;
/// project a point from 3d CAMERA space to the camera local plane
inline vcg::Point2<S> Project(const vcg::Point3<S> & p) const;
/// transforms local plane coords to vieport (pixel) coords
inline vcg::Point2<S> LocalToViewportPx(const vcg::Point2<S> & p) const;
/// unproject a point from the camera local plane (plus depth) to 3d CAMERA space
inline vcg::Point3<S> UnProject(const vcg::Point2<S> & p, const S & d) const;
/// transforms vieport (pixel) coords to local plane coords
inline vcg::Point2<S> ViewportPxToLocal(const vcg::Point2<S> & p) const;
/// transforms local plane coords to vieport (pixel) coords
inline vcg::Point2<S> LocalToViewportPx(const vcg::Point2<S> & p) const;
/// transforms vieport (pixel) coords to [-1 1] coords
inline vcg::Point2<S> ViewportPxTo_neg1_1(const vcg::Point2<S> & p) const;
/// transforms vieport (pixel) coords to local plane coords
inline vcg::Point2<S> ViewportPxToLocal(const vcg::Point2<S> & p) const;
/// transforms [-1 1] coords to vieport (pixel) coords MICHELE IO
inline vcg::Point2<S> Neg1_1ToViewportPx(const vcg::Point2<S> & p) const;
/// transforms vieport (pixel) coords to [-1 1] coords
inline vcg::Point2<S> ViewportPxTo_neg1_1(const vcg::Point2<S> & p) const;
/// transforms local plane coords to [0 1] coords
inline vcg::Point2<S> LocalTo_0_1(const vcg::Point2<S> & p) const;
/// transforms [-1 1] coords to vieport (pixel) coords MICHELE IO
inline vcg::Point2<S> Neg1_1ToViewportPx(const vcg::Point2<S> & p) const;
/// transforms local plane coords to [-1 1] coords
inline vcg::Point2<S> LocalTo_neg1_1(const vcg::Point2<S> & p) const;
/// transforms local plane coords to [0 1] coords
inline vcg::Point2<S> LocalTo_0_1(const vcg::Point2<S> & p) const;
/// transforms an undistorted 2D camera plane point in a distorted 2D camera plane point
vcg::Point2<S> UndistortedToDistorted(vcg::Point2<S> u) const;
/// transforms local plane coords to [-1 1] coords
inline vcg::Point2<S> LocalTo_neg1_1(const vcg::Point2<S> & p) const;
/// transforms a distorted 2D camera plane point in an undistorted 2D camera plane point
vcg::Point2<S> DistortedToUndistorted(vcg::Point2<S> d) const;
//--------------------------------
/// transforms an undistorted 2D camera plane point in a distorted 2D camera plane point
vcg::Point2<S> UndistortedToDistorted(vcg::Point2<S> u) const;
/// transforms a distorted 2D camera plane point in an undistorted 2D camera plane point
vcg::Point2<S> DistortedToUndistorted(vcg::Point2<S> d) const;
//--------------------------------
};
@ -249,189 +252,224 @@ public:
template<class S>
vcg::Point2<S> Camera<S>::Project(const vcg::Point3<S> & p) const
{
vcg::Point2<S> q = Point2<S>(p[0],p[1]);
vcg::Point2<S> d = Point2<S>(p[0],p[1]);
vcg::Point2<S> q = Point2<S>(p[0],p[1]);
vcg::Point2<S> d = Point2<S>(p[0],p[1]);
if(!IsOrtho())
{
q[0] *= FocalMm/p.Z();
q[1] *= FocalMm/p.Z();
if(!IsOrtho())
{
q[0] *= FocalMm/p.Z();
q[1] *= FocalMm/p.Z();
if(k[0]!=0)
{
vcg::Point2<S> d;
d=UndistortedToDistorted(q);
q=d;
}
if(k[0]!=0)
{
vcg::Point2<S> d;
d=UndistortedToDistorted(q);
q=d;
}
}
}
return q;
return q;
}
template <class S> vcg::Matrix44<S> Camera<S>::GetMatrix(S nearVal, S farVal) {
S left, right, bottom, top, nr;
GetFrustum(left, right, bottom,top, nr);
if(cameraType == PERSPECTIVE) {
S ratio = nearVal/nr;
left *= ratio;
right *= ratio;
bottom *= ratio;
top *= ratio;
}
vcg::Matrix44<S> m;
m[0][0] = 2.0*nearVal/(right - left);
m[0][1] = 0;
m[0][2] = (right + left)/(right - left);
m[0][3] = 0;
m[1][0] = 0;
m[1][1] = 2*nearVal/(top - bottom);
m[1][2] = (top + bottom)/(top - bottom);
m[1][3] = 0;
m[2][0] = 0;
m[2][1] = 0;
m[2][2] = -(farVal + nearVal)/(farVal - nearVal);
m[2][3] = - 2*farVal*nearVal/(farVal - nearVal);
m[3][0] = 0;
m[3][1] = 0;
m[3][2] = -1;
m[3][3] = 0;
return m;
}
/// unproject a point from the camera 2d plane [-1,-1]x[1,1] (plus depth) to 3d CAMERA space
template<class S>
vcg::Point3<S> Camera<S>::UnProject(const vcg::Point2<S> & p, const S & d) const
{
vcg::Point3<S> np = Point3<S>(p[0], p[1], d);
vcg::Point3<S> np = Point3<S>(p[0], p[1], d);
if(!IsOrtho())
{
if(k[0]!=0)
{
vcg::Point2<S> d = Point2<S>(p[0], p[1]);
vcg::Point2<S> u=DistortedToUndistorted(d);
np[0]=u[0];
np[1]=u[1];
}
if(!IsOrtho())
{
if(k[0]!=0)
{
vcg::Point2<S> d = Point2<S>(p[0], p[1]);
vcg::Point2<S> u=DistortedToUndistorted(d);
np[0]=u[0];
np[1]=u[1];
}
np[0] /= FocalMm/d;
np[1] /= FocalMm/d;
}
np[0] /= FocalMm/d;
np[1] /= FocalMm/d;
}
return np;
return np;
}
/// transforms local plane coords to vieport (pixel) coords
template<class S>
vcg::Point2<S> Camera<S>::LocalToViewportPx(const vcg::Point2<S> & p) const
{
vcg::Point2<S> np;
vcg::Point2<S> np;
np[0] = (p[0] / PixelSizeMm.X()) + CenterPx.X();
np[1] = (p[1] / PixelSizeMm.Y()) + CenterPx.Y();
np[0] = (p[0] / PixelSizeMm.X()) + CenterPx.X();
np[1] = (p[1] / PixelSizeMm.Y()) + CenterPx.Y();
return np;
return np;
}
/// transforms vieport (pixel) coords to local plane coords
template<class S>
vcg::Point2<S> Camera<S>::ViewportPxToLocal(const vcg::Point2<S> & p) const
{
vcg::Point2<S> ps;
ps[0] = (p[0]-CenterPx.X()) * PixelSizeMm.X();
ps[1] = (p[1]-CenterPx.Y()) * PixelSizeMm.Y();
return ps;
vcg::Point2<S> ps;
ps[0] = (p[0]-CenterPx.X()) * PixelSizeMm.X();
ps[1] = (p[1]-CenterPx.Y()) * PixelSizeMm.Y();
return ps;
}
/// transforms vieport (pixel) coords to [-1 1] coords
template<class S>
vcg::Point2<S> Camera<S>::ViewportPxTo_neg1_1(const vcg::Point2<S> & p) const
{
vcg::Point2<S> ps;
ps[0] = 2.0f * ((p[0]-CenterPx.X()) * PixelSizeMm.X())/ ( PixelSizeMm.X() * (S)ViewportPx[0] );
ps[1] = 2.0f * ((p[1]-CenterPx.Y()) * PixelSizeMm.Y())/ ( PixelSizeMm.Y() * (S)ViewportPx[1] );
return ps;
vcg::Point2<S> ps;
ps[0] = 2.0f * ((p[0]-CenterPx.X()) * PixelSizeMm.X())/ ( PixelSizeMm.X() * (S)ViewportPx[0] );
ps[1] = 2.0f * ((p[1]-CenterPx.Y()) * PixelSizeMm.Y())/ ( PixelSizeMm.Y() * (S)ViewportPx[1] );
return ps;
}
/// transforms [-1 1] coords to vieport (pixel) coords MICHELE IO
template<class S>
vcg::Point2<S> Camera<S>::Neg1_1ToViewportPx(const vcg::Point2<S> & p) const
{
vcg::Point2<S> ps;
ps[0] = ((PixelSizeMm.X() * (S)ViewportPx[0] *p[0])/(2.0f * PixelSizeMm.X()))+CenterPx.X();
ps[1] = ((PixelSizeMm.Y() * (S)ViewportPx[1] *p[1])/(2.0f * PixelSizeMm.Y()))+CenterPx.Y();
return ps;
vcg::Point2<S> ps;
ps[0] = ((PixelSizeMm.X() * (S)ViewportPx[0] *p[0])/(2.0f * PixelSizeMm.X()))+CenterPx.X();
ps[1] = ((PixelSizeMm.Y() * (S)ViewportPx[1] *p[1])/(2.0f * PixelSizeMm.Y()))+CenterPx.Y();
return ps;
}
/// transforms local plane coords to [0-1] coords
template<class S>
vcg::Point2<S> Camera<S>::LocalTo_0_1(const vcg::Point2<S> & p) const
{
vcg::Point2<S> ps;
ps[0] = ( p[0]/PixelSizeMm.X() + CenterPx.X() ) / (S)ViewportPx[0];
ps[1] = ( p[1]/PixelSizeMm.Y() + CenterPx.Y() ) / (S)ViewportPx[1];
return ps;
vcg::Point2<S> ps;
ps[0] = ( p[0]/PixelSizeMm.X() + CenterPx.X() ) / (S)ViewportPx[0];
ps[1] = ( p[1]/PixelSizeMm.Y() + CenterPx.Y() ) / (S)ViewportPx[1];
return ps;
}
/// transforms local plane coords to [-1 1] coords
template<class S>
vcg::Point2<S> Camera<S>::LocalTo_neg1_1(const vcg::Point2<S> & p) const
{
vcg::Point2<S> ps;
ps[0] = 2.0f * p[0] / ( PixelSizeMm.X() * (S)ViewportPx[0] );
ps[1] = 2.0f * p[1] / ( PixelSizeMm.Y() * (S)ViewportPx[1] );
return ps;
vcg::Point2<S> ps;
ps[0] = 2.0f * p[0] / ( PixelSizeMm.X() * (S)ViewportPx[0] );
ps[1] = 2.0f * p[1] / ( PixelSizeMm.Y() * (S)ViewportPx[1] );
return ps;
}
/// transforms an undistorted 2D camera plane point in a distorted 2D camera plane point
template<class Scalar>
vcg::Point2<Scalar> Camera<Scalar>::UndistortedToDistorted(vcg::Point2<Scalar> u) const
{
vcg::Point2<Scalar> dis;
vcg::Point2<Scalar> dc=ViewportPxTo_neg1_1(DistorCenterPx);
const Scalar SQRT3 = Scalar(1.732050807568877293527446341505872366943);
const Scalar CBRT = Scalar(0.33333333333333333333333);
Scalar Ru,Rd,lambda,c,d,Q,R,D,S,T,sinT,cosT;
{
vcg::Point2<Scalar> dis;
vcg::Point2<Scalar> dc=ViewportPxTo_neg1_1(DistorCenterPx);
const Scalar SQRT3 = Scalar(1.732050807568877293527446341505872366943);
const Scalar CBRT = Scalar(0.33333333333333333333333);
Scalar Ru,Rd,lambda,c,d,Q,R,D,S,T,sinT,cosT;
if(((u[0]-dc[0])==0 && (u[1]-dc[1])==0) || k[0] == 0)
{
dis[0] = u[0];
dis[1] = u[1];
return dis;
}
if(((u[0]-dc[0])==0 && (u[1]-dc[1])==0) || k[0] == 0)
{
dis[0] = u[0];
dis[1] = u[1];
return dis;
}
Ru = hypot ((u[0]-dc[0]), (u[1]-dc[1])); /* SQRT(Xu*Xu+Yu*Yu) */
c = 1 / k[0];
d = -c * Ru;
Ru = hypot ((u[0]-dc[0]), (u[1]-dc[1])); /* SQRT(Xu*Xu+Yu*Yu) */
c = 1 / k[0];
d = -c * Ru;
Q = c / 3;
R = -d / 2;
if (R<0)
D = pow(Q,3) + sqrt(-R);
else
D = pow(Q,3) + sqrt(R);
Q = c / 3;
R = -d / 2;
if (R<0)
D = pow(Q,3) + sqrt(-R);
else
D = pow(Q,3) + sqrt(R);
if (D >= 0) /* one real root */
{
D = sqrt(D);
S = pow((R + D),CBRT);
if (R>=D)
T = pow((R - D),CBRT);
else
T = - pow(abs((int)(R - D)),CBRT); //MODIFICATO DA ME
Rd = S + T;
if (D >= 0) /* one real root */
{
D = sqrt(D);
S = pow((R + D),CBRT);
if (R>=D)
T = pow((R - D),CBRT);
else
T = - pow(abs((int)(R - D)),CBRT); //MODIFICATO DA ME
Rd = S + T;
if (Rd < 0)
Rd = sqrt(-1 / (3 * k[0]));
}
else /* three real roots */
{
D = sqrt(-D);
S = pow((Scalar)(hypot (R, D)),(Scalar)CBRT);
T = atan2 (D, R) / 3;
//SinCos(T, sinT, cosT);
sinT=sin(T);
cosT=cos(T);
if (Rd < 0)
Rd = sqrt(-1 / (3 * k[0]));
}
else /* three real roots */
{
D = sqrt(-D);
S = pow((Scalar)(hypot (R, D)),(Scalar)CBRT);
T = atan2 (D, R) / 3;
//SinCos(T, sinT, cosT);
sinT=sin(T);
cosT=cos(T);
/* the larger positive root is 2*S*cos(T) */
/* the smaller positive root is -S*cos(T) + SQRT(3)*S*sin(T) */
/* the negative root is -S*cos(T) - SQRT(3)*S*sin(T) */
Rd = -S * cosT + SQRT3 * S * sinT; /* use the smaller positive root */
}
/* the larger positive root is 2*S*cos(T) */
/* the smaller positive root is -S*cos(T) + SQRT(3)*S*sin(T) */
/* the negative root is -S*cos(T) - SQRT(3)*S*sin(T) */
Rd = -S * cosT + SQRT3 * S * sinT; /* use the smaller positive root */
}
lambda = Rd / Ru;
lambda = Rd / Ru;
dis[0] = u[0] * lambda;
dis[1] = u[1] * lambda;
dis[0] = u[0] * lambda;
dis[1] = u[1] * lambda;
return dis;
}
return dis;
}
/// transforms a distorted 2D camera plane point in an undistorted 2D camera plane point
template<class S>
vcg::Point2<S> Camera<S>::DistortedToUndistorted(vcg::Point2<S> d) const
{
vcg::Point2<S> u;
vcg::Point2<S> dc=ViewportPxTo_neg1_1(DistorCenterPx);
S r=sqrt(pow((d[0]-dc[0]),2)+pow((d[1]-dc[1]),2));
u[0]=d[0]*(1-k[0]*r*r);
u[1]=d[1]*(1-k[0]*r*r);
{
vcg::Point2<S> u;
vcg::Point2<S> dc=ViewportPxTo_neg1_1(DistorCenterPx);
S r=sqrt(pow((d[0]-dc[0]),2)+pow((d[1]-dc[1]),2));
u[0]=d[0]*(1-k[0]*r*r);
u[1]=d[1]*(1-k[0]*r*r);
return u;
return u;
}
}
//--- basic camera setup (GL-like)
@ -440,36 +478,36 @@ vcg::Point2<S> Camera<S>::DistortedToUndistorted(vcg::Point2<S> d) const
template<class S>
void Camera<S>::SetPerspective( S AngleDeg, S AspectRatio, S Focal, vcg::Point2<int> Viewport)
{
cameraType = PERSPECTIVE;
S halfsize[2];
cameraType = PERSPECTIVE;
S halfsize[2];
halfsize[1] = tan(math::ToRad(AngleDeg/2.0f)) * Focal;
halfsize[0] = halfsize[1]*AspectRatio;
halfsize[1] = tan(math::ToRad(AngleDeg/2.0f)) * Focal;
halfsize[0] = halfsize[1]*AspectRatio;
SetFrustum(-halfsize[0],halfsize[0],-halfsize[1],halfsize[1],Focal,Viewport);
SetFrustum(-halfsize[0],halfsize[0],-halfsize[1],halfsize[1],Focal,Viewport);
}
/// set the camera specifying the frustum view
template<class S>
void Camera<S>::SetFrustum( S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport)
{
S vp[2];
vp[0] = dx-sx;
vp[1] = tp-bt;
S vp[2];
vp[0] = dx-sx;
vp[1] = tp-bt;
ViewportPx[0] = Viewport[0];
if(vp[1] != -1)
ViewportPx[1] = Viewport[1]; // the user specified the viewport
else
ViewportPx[1] = ViewportPx[0]; // default viewport
ViewportPx[0] = Viewport[0];
if(vp[1] != -1)
ViewportPx[1] = Viewport[1]; // the user specified the viewport
else
ViewportPx[1] = ViewportPx[0]; // default viewport
PixelSizeMm[0] = vp[0] / (S)Viewport[0];
PixelSizeMm[1] = vp[1] / (S)Viewport[1];
PixelSizeMm[0] = vp[0] / (S)Viewport[0];
PixelSizeMm[1] = vp[1] / (S)Viewport[1];
CenterPx[0] = -sx/vp[0] * (S)Viewport[0];
CenterPx[1] = -bt/vp[1] * (S)Viewport[1];
CenterPx[0] = -sx/vp[0] * (S)Viewport[0];
CenterPx[1] = -bt/vp[1] * (S)Viewport[1];
FocalMm =Focal;
FocalMm =Focal;
}
//--- special cameras setup
@ -478,29 +516,29 @@ void Camera<S>::SetFrustum( S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Vi
template<class S>
void Camera<S>::SetCavalieri(S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport)
{
cameraType = CAVALIERI;
SetFrustum(sx, dx, bt, tp, Focal,Viewport);
cameraType = CAVALIERI;
SetFrustum(sx, dx, bt, tp, Focal,Viewport);
}
/// set the camera specifying the isometric view
template<class S>
void Camera<S>::SetIsometric(S sx, S dx, S bt, S tp, S Focal, vcg::Point2<int> Viewport)
{
cameraType = ISOMETRIC;
SetFrustum(sx, dx, bt, tp, Focal,Viewport);
cameraType = ISOMETRIC;
SetFrustum(sx, dx, bt, tp, Focal,Viewport);
}
/// returns the frustum
template<class S>
void Camera<S>:: GetFrustum( S & sx, S & dx, S & bt, S & tp, S & nr)
{
dx = CenterPx.X()* PixelSizeMm.X(); //scaled center
sx = -( (S)ViewportPx.X() - CenterPx.X() ) * PixelSizeMm.X();
dx = CenterPx.X()* PixelSizeMm.X(); //scaled center
sx = -( (S)ViewportPx.X() - CenterPx.X() ) * PixelSizeMm.X();
bt = -CenterPx.Y()* PixelSizeMm.Y();
tp = ( (S)ViewportPx.Y() - CenterPx.Y() ) * PixelSizeMm.Y();
bt = -CenterPx.Y()* PixelSizeMm.Y();
tp = ( (S)ViewportPx.Y() - CenterPx.Y() ) * PixelSizeMm.Y();
nr = FocalMm;
nr = FocalMm;
}
}