raygeo.geo.algo.interp

Segment interpolation utilities for parameter-based point projection, clipping, and scanline data slicing along 3D line segments.

Functions

barycentric_interpolate()

barycentric_interpolate(
    p: tuple[float, float],
    va: tuple[float, float],
    vb: tuple[float, float],
    vc: tuple[float, float],
    ua: float,
    ub: float,
    uc: float,
) -> float

Interpolate a scalar field at a point inside a triangle.

Given triangle vertices (va, vb, vc) with scalar values (ua, ub, uc), returns the linearly interpolated value at point p using barycentric coordinates.

Parameter	Type	Description
p	tuple[float, float]	Query point (x, y).
va	tuple[float, float]	First triangle vertex (x, y).
vb	tuple[float, float]	Second triangle vertex (x, y).
vc	tuple[float, float]	Third triangle vertex (x, y).
ua	float	Scalar value at vertex a.
ub	float	Scalar value at vertex b.
uc	float	Scalar value at vertex c.
Returns	float	Interpolated scalar value. Outside the triangle, the barycentric coordinates are clamped to [0, 1].
Complexity		O(1) time, O(1) space

compute_segment_delta_3d()

compute_segment_delta_3d(
    start: tuple[float, float, float],
    end: tuple[float, float, float],
) -> tuple[float, float, float, float]

Compute delta vector and squared length between two 3D points.

Parameter	Type	Description
start	tuple[float, float, float]	Starting point (x, y, z).
end	tuple[float, float, float]	Ending point (x, y, z).
Returns	tuple[float, float, float, float]	(dx, dy, dz, len_sq).
Complexity		O(1) time, O(1) space

compute_t_range()

compute_t_range(
    origin: tuple[float, float, float],
    new_start: tuple[float, float, float],
    new_end: tuple[float, float, float],
    delta: tuple[float, float, float, float],
) -> tuple[float, float]

Compute parameter range (t_start, t_end) for a clipped sub-segment.

Parameter	Type	Description
origin	tuple[float, float, float]	Start of original segment (x, y, z).
new_start	tuple[float, float, float]	Start of clipped sub-segment (x, y, z).
new_end	tuple[float, float, float]	End of clipped sub-segment (x, y, z).
delta	tuple[float, float, float, float]	Segment delta from compute_segment_delta_3d.
Returns	tuple[float, float]	(t_start, t_end) in [0, 1].
Complexity		O(1) time, O(1) space

get_barycentric_weights()

get_barycentric_weights(
    p: tuple[float, float],
    va: tuple[float, float],
    vb: tuple[float, float],
    vc: tuple[float, float],
) -> tuple[float, float, float]

Compute raw barycentric coordinates for a point in a triangle.

Returns (r, s, t) where r is the weight for va, s for vb, t for vc. Weights are unclamped — the point is strictly inside (or on the boundary of) the triangle iff all three are in [0, 1].

Parameter	Type	Description
p	tuple[float, float]	Query point (x, y).
va	tuple[float, float]	First triangle vertex (x, y).
vb	tuple[float, float]	Second triangle vertex (x, y).
vc	tuple[float, float]	Third triangle vertex (x, y).
Returns	tuple[float, float, float]	Tuple (r, s, t) of raw barycentric coordinates.
Complexity		O(1) time, O(1) space

project_t_along_segment()

project_t_along_segment(
    origin: tuple[float, float, float],
    point: tuple[float, float, float],
    delta: tuple[float, float, float, float],
) -> float

Project a point onto a line segment, returning t in [0, 1].

Parameter	Type	Description
origin	tuple[float, float, float]	Start of segment (x, y, z).
point	tuple[float, float, float]	Point to project (x, y, z).
delta	tuple[float, float, float, float]	Segment delta from compute_segment_delta_3d.
Returns	float	Parameter t clamped to [0, 1].
Complexity		O(1) time, O(1) space

slice_scanline_data()

slice_scanline_data(data: list[int], t_start: float, t_end: float) -> list[int]

Slice a scanline power array by parameter range [t_start, t_end).

Parameter	Type	Description
data	list[int]	Full scanline power values.
t_start	float	Start parameter in [0, 1].
t_end	float	End parameter in [0, 1].
Returns	list[int]	Sliced power values.
Complexity		O(n) time, O(n) space where n is the length of the data slice

solve_quadratic()

solve_quadratic(
    a: float,
    b: float,
    c: float,
) -> tuple[float | None, float | None]

Solve quadratic equation a x^2 + b x + c = 0.

Parameter	Type	Description
a	float	Quadratic coefficient.
b	float	Linear coefficient.
c	float	Constant term.
Returns	tuple[float | None, float | None]	(root1, root2), each None if no real root.
Complexity		O(1) time, O(1) space