How to convert a 3D point on a plane to UV coordinates?

How to convert a 3D point on a plane to UV coordinates?

I have a 3d point, defined by [x0, y0, z0]. This point belongs to a plane, defined by [a, b, c, d]. How can convert or map the 3d point to a pair of (u,v) coordinates ? This must be something really simple, but I can’t figure it out.

How to convert azimuth / elevation angles to u / v coordinates?

UV = azel2uv (AzEl) converts the azimuth/elevation angle pairs to their corresponding coordinates in u / v space. Find the corresponding uv representation for 30° azimuth and 0° elevation. Azimuth and elevation angles, specified as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [azimuth; elevation].

How to find the you / v coordinates for a vector?

This figure illustrates the azimuth angle and elevation angle for a vector shown as a green solid line. The u/v coordinates for the positive hemisphere x ≥ 0 can be derived from the phi and theta angles. In these expressions, φ and θ are the phi and theta angles, respectively.

How to convert UV to azel2uv in Excel?

UV = azel2uv (AzEl) converts the azimuth/elevation angle pairs to their corresponding coordinates in u / v space. Find the corresponding uv representation for 30° azimuth and 0° elevation. Azimuth and elevation angles, specified as a two-row matrix.

How are the coordinates of a 3D point determined?

By default, the coordinates of a 3D point are defined with respect to the world coordinate system. The world coordinate system though, is just one among an infinity of possible coordinate systems.

How to check if a point is within a 3D triangle?

A general plane equation is Ax + By + Cz = D. The 3-dimensional vector < A,B,C > is perpendicular to the plane. (Note that there is not a unique equation of this form; you can multiply the equation by any nonzero number and get another equation of the plane.

When is the point P exactly at a vertex of the triangle?

When one of α, β, γ is 1 and the other two are 0, then the point P is exactly at a vertex of the triangle. Of course, these computations assume P is already in the plane of the triangle. If P is not in the plane of the triangle, then you should project it there first, before computing the barycentric coordinates.

How are the texture coordinates of a pixel determined?

The texture coordinates at each pixel are easily determined by interpolating the coordinates stored at each vertex: The pixel at (0,0) coincides with the vertex at (0, 0); therefore, the texture coordinates at that pixel are simply the texture coordinates stored at that vertex, UV (0.0, 0.0).

How to map Texel cells to pixel cells?

By simply shifting the x and y quad coordinates by -0.5 units, texel cells will perfectly cover pixel cells and the quad can be perfectly recreated on the screen. (The last illustration in this topic shows the quad at the corrected coordinates.)

Where is the screen space coordinate on a pixel?

The preceding diagram correctly shows each physical pixel as a point in the center of each cell. The screen space coordinate (0, 0) is located directly at the top-left pixel, and therefore at the center of the top-left cell.