Quick guide
How to use this calculator
- Select a supported direction or geometric form when modes are available.
- Enter the labelled coordinates, coefficients, distances, or transformation parameters.
- Read the primary result, then inspect classification, equation, closest-point, or graph details.
Calculation method
Apply the coordinate relationship
P=(nP₁+mP₂)/(m+n).
The calculator validates degenerate points, lines, planes, conics, coordinate-system domains, and bounded graph sampling before reporting a result.
Worked example
Worked example
A 1:1 ratio gives the midpoint.
P=(nP₁+mP₂)/(m+n).
Supported inputs
Precision and limits
Coordinate conventions
Cartesian coordinates use right-handed x, y, z axes. Polar and cylindrical azimuth is measured counterclockwise from positive x; spherical φ is the polar angle from positive z.
Numerical range
Inputs may be zero or have magnitude from 1e-100 through 1e100. Trigonometric angles are limited to ±1e9°. Fixed-step plots limit Lissajous frequencies to ±20 and polar frequencies to ±30, preserving at least 12 samples per cycle. Generated grids and plots use explicit point caps.
Precision and graphs
Calculations use double-precision arithmetic and normally display 12 significant digits. Graphs are bounded numerical visualizations, not proofs of global behavior.