Saltire logo CoreGX

The Geometry Engine

CoreGX is powered by the same constraint solver and symbolic algebra system at the heart of Geometry Expressions, a commercial symbolic geometry tool with decades of development behind it. The engine is exposed here as a REST API, making precise geometric computation available to any application or LLM that can make an HTTP request.

Describe relationships, not coordinates

Most geometry tools require you to place objects at explicit positions. CoreGX works the other way: you describe the relationships between objects, and the engine determines where everything goes.

Specify that a triangle has a right angle at B, that sides AB and BC have lengths 3 and 4, and that a circle passes through all three vertices. The engine resolves the full figure from those constraints alone, without you ever naming a coordinate.

This makes CoreGX well suited to tasks where the geometry is defined by rules rather than measurements: proofs, constructions, and figures that need to hold under symbolic parameters.

constraints, not coordinates
# No x/y coordinates needed.
# Describe the figure by its rules.
anglemode degree
triangle A B C
angle A B C 90
distance AB 3
distance BC 4
circumcircle C0 O A B C
measure distance(O,A)
measure area(A,B,C)

Exact, symbolic results

Numerical solvers approximate. CoreGX computes exactly. When a measurement depends on a symbolic parameter, the result is a symbolic expression, not a rounded decimal. Distances, angles, areas, perimeters, and curve equations are returned in closed algebraic form when possible.

A right triangle with legs a and b returns a hypotenuse of sqrt(a^2 + b^2), not 5.000. This precision is preserved through the full computation, making results suitable for mathematical publishing, LLM reasoning, or downstream symbolic computation.

symbolic parameters in, exact expressions out
# Legs are symbolic: a and b
anglemode degree
triangle A B C
angle A B C 90
distance AB a
distance BC b
measure distance(A,C)
measure area(A,B,C)

# Response equations:
# sqrt(a^2+b^2)
# (1/2)*a*b

What the engine handles

A summary of supported constructions and constraints.

Shapes

Points, lines, segments, circles, triangles, polygons, vectors, and cyclic polygons.

Derived constructions

Midpoints, intersections, altitudes, medians, angle bisectors, perpendicular bisectors, projections, circumcircles, incircles, and excircles.

Constraints

Distance, angle, radius, parallelism, perpendicularity, congruence, incidence, tangency, and side/orientation constraints.

Curves

Ellipses, parabolas, hyperbolas, loci, envelopes, Cartesian functions, polar functions, and parametric curves.

Transforms

Reflection, rotation, dilation, and translation, applied to any object. Transforms may depend on parameters, enabling locus and envelope constructions.

Measurements

Distance, angle, area, perimeter, radius, slope, direction, coordinates, line and circle equations, parametric equations, centroids, and moments of inertia.

Ready to use it?

The language reference covers the full command set. The API docs describe the single endpoint you need. Request a key to get started.

Request API Key