Module rules 

Residual builders for the supported rule classes.

Linear rules: fix, equal, linear relation (sum/difference/ratio/min/max with constant coefficients), equal spacing.

Geometric rules: coincident, horizontal, vertical, fixed point, distance (point–point, signed point–line), point on line/circle, length, equal length, parallel, perpendicular, angle, concentric, radius, equal radius, line–circle and circle–circle tangency.

Every builder returns residual rows; the solver decides linearity from the expressions themselves. Residuals of direction rules are normalized (sine/cosine of angles) so their scale is 1 regardless of segment length.

Enums

CircleTangency

Tangency between two circles.

Cmp

Linear comparison operators.

Functions

all_equal

Equal values: v₀ = v₁ = ….

angle

Signed angle from segment 1 to segment 2 equals theta (radians). The residual is the wrapped angle difference, smooth everywhere except at ±π.

at_least

a ≥ min.

at_most

a ≤ max.

coincident

Coincident points.

concentric

Concentric circles/arcs.

distance

|q − p| = d.

distance_cmp

|q − p| (cmp) d.

equal

a = b.

equal_length

Equal segment lengths.

equal_radius

Equal radii.

equal_spacing

Consecutive differences are equal: v₁−v₀ = v₂−v₁ = ….

fix

v = value.

fix_point

Point fixed at a location.

horizontal

Same Y.

length

Segment length.

linear

Σ cᵢ·eᵢ (cmp) rhs.

parallel

Parallel (or anti-parallel) segments: sin(angle) = 0.

perpendicular

Perpendicular segments: cos(angle) = 0.

point_line_distance

Signed point–line distance equals d (sign selects the side).

point_on_circle

Point lies on the circle (c, r).

point_on_line

Point lies on the infinite line through a, b.

polar_point

Point expression of an arc/circle point at an angle: c + r·(cos a, sin a).

radius

Radius equals value.

ratio

a = k · b (constant ratio).

signed_line_distance

Signed distance from p to the line a → b (positive on the left).

tangent_circles

Circle–circle tangency.

tangent_line_circle

Line a → b tangent to circle (c, r); side (±1) keeps the circle on its current side of the line.

v

Convenience: variable expression.

vertical

Same X.