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is the rotation matrix by which b is rotated in relation to a; t is the translation vector from a to b; n and d are the normal vector of the plane and the distance from origin to the plane respectively. K a and K b are the cameras' intrinsic parameter matrices. The figure shows camera b looking at the plane at distance d.
The camera matrix derived in the previous section has a null space which is spanned by the vector = This is also the homogeneous representation of the 3D point which has coordinates (0,0,0), that is, the "camera center" (aka the entrance pupil; the position of the pinhole of a pinhole camera) is at O.
The angle rotation sequence is ψ, θ, φ. Note that in this case ψ > 90° and θ is a negative angle. Similarly for Euler angles, we use the Tait Bryan angles (in terms of flight dynamics): Heading – : rotation about the Z-axis; Pitch – : rotation about the new Y-axis
Homogeneous coordinates are ubiquitous in computer graphics because they allow common vector operations such as translation, rotation, scaling and perspective projection to be represented as a matrix by which the vector is multiplied. By the chain rule, any sequence of such operations can be multiplied out into a single matrix, allowing simple ...
Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...
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Rotating the image plane (as by adjusting the back or rear standard on a view camera) alters perspective (e.g., the sides of a building converge), but works with a lens that has a smaller image circle. Rotation of the lens or back about a horizontal axis is commonly called tilt, and rotation about a vertical axis is commonly called swing.
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