mt.geo2d.linear

Module supporting the 2x2 linear transformation.

Functions

• mat2sshr(): Converts a 2d transformation matrix into an sshr tuple.

• mat2sshr_tf(): Converts an array of 2x2 transformation matrices into an array of sshr tuples.

• sshr2mat(): Converts an sshr tuple into a mat2 transformation matrices.

• sshr2mat_tf(): Converts an array of sshr tuples into an array of 2x2 transformation matrices.

• make_affine(): Makes an array of 2d affine transformation matrices (in 3x3 with [0,0,1] as the 3rd row).

mt.geo2d.linear.mat2sshr(m: mat2x2) → vec4

Converts a 2d transformation matrix into an sshr tuple.

An sshr tuple (sx,sy,h,r) represents the scale2d(sx,sy) shear2d(h) rotate2d(r) transformation.

Formula:

[[a0, a1], [a2, a3]] = m  # row-major
sy = hypot(a2,a3)
r = atan2(a2,a3)
sx = det(A)/sy
h = (a0*a2 + a1*a3)/(sx*r)

Parameters:

m (glm.mat2) – the input 2d transformation matrix

Returns:

sshr – the output sshr tuple

Return type:

glm.vec4

References

[1]

Pham et al, Distances and Means of Direct Similarities, IJCV, 2015. (not really, cheeky MT is trying to advertise his paper!)

mt.geo2d.linear.mat2sshr_tf(tensor)

Converts an array of 2x2 transformation matrices into an array of sshr tuples.

An sshr tuple (sx,sy,h,r) represents the scale2d(sx,sy) shear2d(h) rotate2d(r) transformation.

Formula:

[[a0, a1], [a2, a3]] = m
sy = hypot(a2,a3)
r = atan2(a2,a3)
sx = det(A)/sy
h = (a0*a2 + a1*a3)/(sx*r)

Parameters:

tensor (tensorflow.Tensor) – a tensor of shape (batch, 2, 2) containing 2d row-major transformation matrices

Returns:

a tensor of shape (batch, 4) containing sshr tuples

Return type:

tensorflow.Tensor

References

[1]

Pham et al, Distances and Means of Direct Similarities, IJCV, 2015. (not really, cheeky MT is trying to advertise his paper!)

mt.geo2d.linear.sshr2mat(sshr: vec4) → mat2x2

Converts an sshr tuple into a mat2 transformation matrices.

An sshr tuple (sx,sy,h,r) represents the scale2d(sx,sy) shear2d(h) rotate2d(r) transformation.

Formula:

cr = cos(r)
sr = sin(r)
a0 = sx*(h*sr + cr)
a1 = sx*(h*cr - sr)
a2 = sy*sr
a3 = sy*cr
m  = [[a0, a1], [a2, a3]]  # row-major

Parameters:

sshr (glm.vec4) – the input sshr tuple

Returns:

the output 2d transformation matrix

Return type:

glm.mat2

References

[1]

Pham et al, Distances and Means of Direct Similarities, IJCV, 2015. (not really, cheeky MT is trying to advertise his paper!)

mt.geo2d.linear.sshr2mat_tf(tensor)

Converts an array of sshr tuples into an array of 2x2 transformation matrices.

An sshr tuple (sx,sy,h,r) represents the scale2d(sx,sy) shear2d(h) rotate2d(r) transformation.

Formula:

cr = cos(r)
sr = sin(r)
a0 = sx*(h*sr + cr)
a1 = sx*(h*cr - sr)
a2 = sy*sr
a3 = sy*cr
m  = [[a0, a1], [a2, a3]]

Parameters:

tensor (tensorflow.Tensor) – a tensor of shape (batch, 4) containing sshr tuples

Returns:

a tensor of shape (batch, 2, 2) containing 2d row-major transformation matrices

Return type:

tensorflow.Tensor

References

[1]

Pham et al, Distances and Means of Direct Similarities, IJCV, 2015. (not really, cheeky MT is trying to advertise his paper!)

mt.geo2d.linear.make_affine(mat2d_tensor, ofs2d_tensor)

Makes an array of 2d affine transformation matrices (in 3x3 with [0,0,1] as the 3rd row).

Parameters:

• mat2d_tensor (tensorflow.Tensor) – a tensor of shape (batch, 2, 2) containing 2d row-major transformation matrices

• ofs2d_tensor (tensorflow.Tensor) – a tensor of shape (batch, 2) containing 2d translations

Returns:

a tensor of shape (batch, 3, 3) containing 2d affine transformation matrices with the linear and translation parts defined in the input tensors

Return type:

tensorflow.Tensor