public abstract class DeformationTransformer extends GeometryTransformer
r
returns its deformed position
f(r)
and the deformation gradient F
at that
location.GeometryTransformer.Constrainer, GeometryTransformer.UndoState, GeometryTransformer.UniformScalingConstrainer
Constructor and Description |
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DeformationTransformer() |
Modifier and Type | Method and Description |
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void |
computeLocalTransforms(Matrix3d PL,
Vector3d Ndiag,
RigidTransform3d T)
Computes the matrices
PL and N that transform
points xl local to a coordinate frame T after
that frame is itself transformed. |
void |
computeTransform(AffineTransform3d XR,
AffineTransform3d X)
Transforms an affine transform
X and returns the result in
XR . |
void |
computeTransform(Matrix3d MR,
Matrix3d M,
Vector3d r)
Transforms a general 3 X 3 matrix
M , located at reference
position r , and returns the result in MR . |
void |
computeTransform(Plane pr,
Plane p,
Vector3d r)
Transforms a plane
p , located at reference position
r , and returns the result in pr . |
void |
computeTransform(RotationMatrix3d RR,
Vector3d Ndiag,
RotationMatrix3d R,
Vector3d r)
Transforms a rotation matrix
R , located at reference
position r , and returns the result in RR . |
void |
computeTransformNormal(Vector3d nr,
Vector3d n,
Vector3d r)
Transforms a normal vector
n , located at a reference
position r , and returns the result in
nr . |
void |
computeTransformPnt(Point3d pr,
Point3d p)
Transforms a point
p and returns the result in
pr . |
void |
computeTransformVec(Vector3d vr,
Vector3d v,
Vector3d r)
Transforms a vector
v , located at a reference
position r , and returns the result in
vr . |
abstract void |
getDeformation(Vector3d p,
Matrix3d F,
Vector3d r)
Computes the deformed position
f(r) and deformation
gradient F for a given reference point r in
undeformed coordinates. |
DeformationTransformer |
getInverse()
Returns
null by since this transformer is not by default
invertible; subclasses my override this. |
boolean |
isAffine()
Returns
false since this transformer does not implement a
linear affine transform. |
boolean |
isInvertible()
Returns
false since this transformer is not by default
invertible; subclasses my override this. |
boolean |
isRigid()
Returns
false since this transformer does not implement a
linear rigid transform. |
computeLinearizedTransform, computeLocalAffineTransform, computeTransform, create, getUndoDataSize, isReflecting, isRestoring, isSaving, popRestoreData, restoreObject, saveObject, setUndoState, transform, transform, transform, transform, transform, transform, transform, transform, transform, transform, transform, transform, transformNormal, transformNormal, transformPnt, transformPnt, transformVec, transformVec, transformWorld, transformWorld
public boolean isRigid()
false
since this transformer does not implement a
linear rigid transform.isRigid
in class GeometryTransformer
public boolean isAffine()
false
since this transformer does not implement a
linear affine transform.isAffine
in class GeometryTransformer
public boolean isInvertible()
false
since this transformer is not by default
invertible; subclasses my override this.isInvertible
in class GeometryTransformer
public DeformationTransformer getInverse()
null
by since this transformer is not by default
invertible; subclasses my override this.getInverse
in class GeometryTransformer
public abstract void getDeformation(Vector3d p, Matrix3d F, Vector3d r)
f(r)
and deformation
gradient F
for a given reference point r
in
undeformed coordinates.p
- if non-null
, returns the deformed positionF
- if non-null
, returns the deformation gradientr
- reference point in undeformed coordinatespublic void computeTransformPnt(Point3d pr, Point3d p)
p
and returns the result in
pr
. The transform is computed according to
pr = f(p)This method provides the low level implementation for point transformations and does not do any saving or restoring of data.
computeTransformPnt
in class GeometryTransformer
pr
- transformed pointp
- point to be transformedpublic void computeTransformVec(Vector3d vr, Vector3d v, Vector3d r)
v
, located at a reference
position r
, and returns the result in
vr
.
The transform is computed according to
vr = F vwhere F is the deformation gradient at the reference position. This method provides the low level implementation for vector transformations and does not do any saving or restoring of data.
computeTransformVec
in class GeometryTransformer
vr
- transformed vectorv
- vector to be transformedr
- reference position of the vector, in original coordinatespublic void computeLocalTransforms(Matrix3d PL, Vector3d Ndiag, RigidTransform3d T)
PL
and N
that transform
points xl
local to a coordinate frame T
after
that frame is itself transformed. The updated local coordinates are
given by
xl' = N PL xlwhere
PL
is symmetric positive definite and
N
is a diagonal matrix that is either the identity,
or a reflection that flips a single axis. See the documentation
for GeometryTransformer.computeLocalTransforms(maspack.matrix.Matrix3d, maspack.matrix.Vector3d, maspack.matrix.RigidTransform3d)
.computeLocalTransforms
in class GeometryTransformer
PL
- primary transformation matrixNdiag
- if non-null, returns the diagonal components of NT
- rigid transform for which the local transforms are computedpublic void computeTransformNormal(Vector3d nr, Vector3d n, Vector3d r)
n
, located at a reference
position r
, and returns the result in
nr
.
The transform is computed according to
-1 T nr = F nwhere F is the deformation gradient at the reference position. The result is not normalized since the unnormalized form could be useful in some contexts. This method provides the low level implementation for normal transformations and does not do any saving or restoring of data.
computeTransformNormal
in class GeometryTransformer
nr
- transformed normaln
- normal to be transformedr
- reference position of the normal, in original coordinatespublic void computeTransform(AffineTransform3d XR, AffineTransform3d X)
X
and returns the result in
XR
. If
[ A p ] X = [ ] [ 0 1 ]the transform is computed according to
[ F A f(p) ] XR = [ ] [ 0 1 ]where f(p) and F are the deformation and deformation gradient at p. This method provides the low level implementation for the transformation of affine transforms and does not do any saving or restoring of data.
computeTransform
in class GeometryTransformer
XR
- transformed transformX
- transform to be transformedpublic void computeTransform(RotationMatrix3d RR, Vector3d Ndiag, RotationMatrix3d R, Vector3d r)
R
, located at reference
position r
, and returns the result in RR
.
The transform is computed according to
RR = RF Rwhere PF RF = F is the left polar decomposition of the deformation gradient at the reference position. This method provides the low level implementation for the transformation of rotation matrices and does not do any saving or restoring of data.
computeTransform
in class GeometryTransformer
RR
- transformed rotationR
- rotation to be transformedr
- reference position of the rotation, in original coordinatesNdiag
- if non-null, returns the diagonal elements of the
matrix N
public void computeTransform(Matrix3d MR, Matrix3d M, Vector3d r)
M
, located at reference
position r
, and returns the result in MR
.
The transform is computed according to
MR = F Mwhere F is the deformation gradient at the reference position. This method provides the low level implementation for the transformation of 3 X 3 matrices and does not do any saving or restoring of data.
computeTransform
in class GeometryTransformer
MR
- transformed matrixM
- matrix to be transformedr
- reference position of the matrix, in original coordinatespublic void computeTransform(Plane pr, Plane p, Vector3d r)
p
, located at reference position
r
, and returns the result in pr
.
Assume that p
is defined by a normal n
and offset o
such that all planar points x
satisfy
n^T x = oThen the transformed normal
nr
and offset or
are computed according to
nr = inv(F)^T n nr = nr / ||nr|| or = nr^T f(r)where F is the deformation gradient at the reference position. This method provides the low level implementation for the transformation of planes and does not do any saving or restoring of data.
computeTransform
in class GeometryTransformer
pr
- transformed planep
- plane to be transformedr
- reference position of the plane, in original coordinates