Points, lines, and coordinate systems
Find the line of intersection of two planes given by ax + by + cz = d or by a point and a normal vector. Returns the direction…
Find the point of intersection of two lines from the slope-intercept form (y = ax + b) or the general form (Ax + By + C =…
Find the latus rectum of a parabola (L = |4p|), an ellipse or a hyperbola (L = 2b²/a) along with the semi-latus rectum, eccentricity,…
Convert between Cartesian (x, y, z) and cylindrical (ρ, θ, z) coordinates of any point in 3D space. Supports degrees and…
Calculate the cosine similarity S_C between two N-dimensional vectors (2 to 8 components) using S_C = (a·b)/(‖a‖‖b‖). Returns…
Write the equation of a sphere in standard form (x−h)²+(y−k)²+(z−l)²=r² or expanded form. Build it from the center and radius,…
Find the coordinates of an unknown point from two known locations and their bearings. Solve intersection (locate a landmark)…
Compute the dot product a · b of two 2D or 3D vectors using a·b = a_x·b_x + a_y·b_y + a_z·b_z. Returns the scalar product,…
Calculate the volume of a parallelepiped from three vectors, four vertices, or edge lengths and angles using the scalar triple…
Compute the cross product a × b of two 3D vectors using a×b = (a_y·b_z − a_z·b_y, a_z·b_x − a_x·b_z, a_x·b_y − a_y·b_x).…
Find the orthogonal (vector) projection of vector a onto vector b using proj = (a·b / b·b) × b. Works for 2D and 3D vectors…
Rotate a point in the coordinate plane around the origin or an arbitrary pivot by any angle. Enter the point, pivot, angle…
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