Qaws

Platform	f32	f64
Linux
macOS
Windows

Qaws (قوس) — Arabic for arc, bow, curve. A dependency-free C11 library for creating, evaluating, sampling, traversing, and inspecting parametric curves and surfaces in 2D and 3D.

One source, four backends: C · HLSL · GLSL · Halide

---

Quick start

#include "qaws.h"

qaws_vec2 pts[] = { {0,0}, {0.3f,1}, {0.7f,1}, {1,0} };
qaws_bezier_desc desc = {
    .dimension = QAWS_DIMENSION_2D,
    .degree = 3,
    .control_points = pts,
    .control_point_count = 4
};

qaws_curve* curve = NULL;
qaws_curve_create_bezier(&desc, &curve);

qaws_eval_result_2d r;
qaws_curve_evaluate_2d(curve, 0.5f, QAWS_EVAL_FLAG_POSITION | QAWS_EVAL_FLAG_D1, &r);
// r.position = point on curve at t=0.5
// r.d1       = first derivative (tangent direction)

qaws_curve_destroy(curve);

Curve families

Every family is created through a descriptor and shares the same evaluation, sampling, traversal, and inspection API after creation.

Family	Degree	Spans	Continuity	Closed	Rational	Dim	Header
Bezier	1..N	1	--	--	--	2D 3D	qaws_bezier.h
Hermite	3	n-1	C1	--	--	2D 3D	qaws_hermite.h
Catmull-Rom	3	n-3 / n	C1	yes	--	2D 3D	qaws_catmull_rom.h
B-Spline	1..N	knot-dep.	C(p-1)	yes	--	2D 3D	qaws_bspline.h
NURBS	1..N	knot-dep.	C(p-1)	yes	yes	2D 3D	qaws_nurbs.h
Trajectory	3	k-1	C1	yes	--	2D 3D	qaws_trajectory.h
Yuksel C2	2	n-1 / n	C2	yes	--	2D 3D	qaws_yuksel.h
Rational Bezier	1..N	1	--	--	yes	2D 3D	qaws_rational_bezier.h
Arc	analytic	seg.	C-inf	opt.	--	2D 3D	qaws_arc.h
Polynomial	1..N	1	C-inf	--	--	2D 3D	qaws_polynomial.h
Clothoid	transcend.	1	C-inf	--	--	2D	qaws_clothoid.h
Subdivision	scheme-dep.	refined	C1..C3	yes	--	2D 3D	qaws_subdivision.h
Composite	per-seg.	seg.	user-dep.	opt.	--	2D 3D	qaws_composite.h

Surfaces

Surface	Header
Bezier patch	qaws_surface_bezier.h
B-Spline	qaws_surface_bspline.h
NURBS	qaws_surface_nurbs.h
Swept (profile along path)	qaws_surface_swept.h
Ruled (linear blend of two curves)	qaws_surface_ruled.h

What you can do

Create

13 curve families + 5 surface types. See the curve families table above.

Evaluate

Capability	Function
Position, D1, D2, D3	qaws_curve_evaluate_2d/3d
Per-span evaluation	qaws_curve_evaluate_span_2d/3d
Batch (SIMD-accelerated)	qaws_curve_evaluate_batch_2d/3d
Surface point + partials + normal	qaws_surface_evaluate

Sample

Mode	Function
Uniform / adaptive	qaws_curve_sample_2d/3d
Curvature-weighted	qaws_curve_sample_curvature_weighted_2d/3d
Feature-preserving	qaws_curve_sample_feature_preserving_2d/3d
Streaming (callback)	qaws_curve_sample_streaming_2d/3d

Traverse

Feature
Modes	parameter, arc-length, timed
Motion profiles	constant speed, constant accel., trapezoidal, S-curve, custom
Easing	10 functions (quad, cubic, sine -- in/out/in-out)
Wrap modes	clamp, loop, ping-pong
Multi-curve	qaws_traversal_create_multi

Inspect

Category	Functions
Geometry	arc length, bounding box, closest point
Differential	tangent, normal, curvature, torsion, speed, Frenet frame
Topology	inflection points, extrema, winding number
Intersection	curve-curve, self-intersection
Visualization	curvature comb

Convert and operate

Conversion	Operations	Export / Import
Hermite -> Bezier	Split at parameter	SVG path data
Catmull-Rom -> Bezier	Join two curves	Polyline export
Bezier -> B-Spline	Offset (2D)	B-spline fitting
B-Spline -> NURBS	Arc-length reparam.	Polyline import
Degree elevation	Reverse
Degree reduction

Multi-backend

The core evaluation math lives in header-only files under src/qaws/core/. These compile on all four backends from the same source:

Backend	What you get	Scalar type
C	Full runtime + prepare + SIMD batch	float or double
HLSL	22 core eval functions	float
GLSL	22 core eval functions	float
Halide	22 core eval functions (symbolic IR)	Halide::Expr

// HLSL compute shader
#include "qaws_hlsl.h"
#include "core/qaws_decasteljau_core.h"

[numthreads(256, 1, 1)]
void CSMain(uint3 id : SV_DispatchThreadID) {
    float t = (float)id.x / (float)(sample_count - 1);
    qaws_vec2 pos = qaws_bezier3_eval_2d(p0, p1, p2, p3, t);
    results[id.x * 2]     = pos.x;
    results[id.x * 2 + 1] = pos.y;
}

Backend detection is automatic (__HLSL_VERSION, GL_core_profile, HALIDE_HALIDERUNTIME_H) or forced via bootstrap headers (qaws_hlsl.h, qaws_glsl.h, qaws_halide.h).

Building

Sharpmake (primary) or CMake (backup).

# CMake
cmake -B build -DQAWS_SCALAR_IS_FLOAT=ON
cmake --build build --config Release
ctest --build-config Release --output-on-failure

# Sharpmake
sharpmake /sources(@'buildsystem/sharpmake/src/main.sharpmake.cs')

Options

Option	Default	Effect
QAWS_SCALAR_IS_FLOAT	ON	float (32-bit) or double (64-bit)
QAWS_ENABLE_SIMD	OFF	AVX2 / SSE2 / NEON batch eval
QAWS_ENABLE_WARNINGS	ON	Compiler warnings
QAWS_WARNINGS_AS_ERRORS	ON(f64) / OFF(f32)	-Werror / /WX

Design

• Zero dependencies -- C11 standard library only (<math.h>, <stdlib.h>, <string.h>)
• Immutable after creation -- qaws_curve and qaws_surface are thread-safe for concurrent reads
• Opaque handles -- all internal state is hidden behind qaws_curve* / qaws_surface*
• Status codes everywhere -- every fallible function returns qaws_status
• Custom allocators -- _ex variants accept qaws_allocator for arena/pool/tracking
• Stack-allocated curves -- qaws_curve_inline for hot paths (no malloc, degree <= 7)

Repository layout

src/qaws/            Public headers and C implementation
src/qaws/core/       Header-only eval kernels (all backends)
src/qaws/internal/   Private implementation details
src/qaws/simd/       SIMD abstraction (AVX2, SSE2, NEON, scalar)
src/qaws/batch/      SIMD batch evaluation
tests/               Test runner
examples/            HLSL, GLSL, Halide shader examples
docs/                Documentation
buildsystem/         Sharpmake project files

Documentation

Full docs are in docs/:

• Overview -- design principles, quick start
• Backends -- C / HLSL / GLSL / Halide architecture
• Curve Families -- all 13 families in detail
• Evaluation -- eval flags, batch eval, core headers, prepare+eval
• Sampling -- uniform, adaptive, curvature-weighted, streaming
• Traversal -- motion profiles, easing, wrap modes
• Inspection -- geometry queries, intersection, analysis
• Building -- CMake and Sharpmake configuration
• Feature Matrix -- function-by-function backend support

License

See LICENSE.