Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as illustrated).

Matrices have two purposes (At least for geometry) Transform things e.g. rotate the car from facing North to facing East Express coordinate system changes e.g. given the driver's location in the …

Coordinate transformations are nonintuitive enough in 2-D, and positively painful in 3-D. This page tackles them in the following order: (i) vectors in 2-D, (ii) tensors in 2-D, (iii) vectors in 3-D, (iv) …

The coordinate transformation and search functionalities are powered by the MapTiler Cloud Coordinates API, which is fully compatible with EPSG.io and also offers a /transform API endpoint for …

This chapter discusses how vectors and matrices are used in robotics to represent 2D and 3D positions, directions, rigid body motion, and coordinate transformations.

After all, two independent observers might well choose coordinate systems with different origins, and different orientations of the coordinate axes. In general, a given vector will have different sets of …

The u-curves of the transformation are the images of vertical lines of the form u = constant and the v-curves are images of horizontal lines of the form v = constant. Together, these curves are called the …

Transformations in coordinate geometry involve changing the position, size, or orientation of a geometric figure. These changes are achieved by applying specific rules or operations to the coordinates of the …

coordinate transformation will usually be given by an equation (x, y) = f(u, v). You can think of it as deforming or moving things in the u-v plane and placing them in the x-y plane.

Some coordinate transformations are simple. For example, the transformation from non-georeferenced plane coordinates to non-georeferenced polar coordinates shown in Figure 2.18.1, below, involves …