Maths utilties
npm install @isopodlabs/mathsA comprehensive TypeScript mathematics library providing vector operations, rationals, complex numbers, quaternions, polynomial solving, and geometric primitives.
``sh`
npm install @isopodlabs/maths
, y, z, w)
- Swizzling support - access vec.xy, vec.xyz, etc.
- Matrix operations - 2x2, 2x3, 3x3, 3x4, 4x4 matrices
- Utility functions - normalize, lerp, project, reflect
- Bounding boxes - extent1, extent2, extent3
- Statistics - mean, variance for scalars and vectors$3
- Basic operations - add, multiply, divide, negate
- BigInt - rationals over bigint
- Generics - rationals over custom types that support arithmetic through add, mul, etc, methods$3
- Basic operations - add, multiply, divide, negate, conjugate
- Transcendental functions - sin, cos, exp, log, sqrt
- Polar form - magnitude, argument, from polar coordinates
- Generics - complex numbers over custom types that support arithmetic through add, mul, etc, methods$3
- Basic operations - add, multiply, divide, negate, conjugate
- Transcendental functions - exp, log
- #### Subclass for unit quaternions ####
- Conversion to/from 3x3 matrix, axis-angle, euler angles$3
- Root finding - real and complex
- Evaluation - single values, arrays, complex numbers
- Operations - add, subtract, multiply, derivative
- Advanced solving - high-degree polynomials use Aberth(complex) or Sturm(real) root finding methods
- Generics - polynomials over custom types that support arithmetic through add, mul, etc, methods$3
- Shapes - lines, circles, Bézier curves (quadratic/cubic)
- Splines - connected sequences of curves
- Utilities - arc length, closest points, intersections
- Curve reduction - convert cubic to quadratic BéziersUsage
$3
`typescript
import { float2, float3 } from '@isopodlabs/maths';// Create vectors
const a = float2(1, 2);
const b = float3(3, 4, 5);
// Vector operations
const sum = a.add(float2(1, 1)); // (2, 3)
const dot = a.dot(float2(2, 3)); // 8
const len = a.len(); // 2.236...
// Swizzling
const swiz = b.xy; // float2(3, 4)
const rev = b.zyx; // float3(5, 4, 3)
// Matrix operations
const m = float2x2(float2(1, 0), float2(0, 1));
const transformed = mul2x2(m, a);
`$3
typescript
import { complex } from '@isopodlabs/maths';const z1 = complex(3, 4); // 3 + 4i
const z2 = complex(1, -1); // 1 - i
const sum = z1.add(z2); // 4 + 3i
const product = z1.mul(z2); // 7 + i
const magnitude = z1.abs(); // 5
const phase = z1.arg(); // 0.927...
// Transcendental functions
const exp_z = complex.exp(z1);
const sin_z = complex.sin(z1);
`$3
typescript
import { polynomial } from '@isopodlabs/maths';// Create polynomial: x² - 5x + 6 = (x-2)(x-3)
const poly = new polynomial([6, -5, 1]);
const roots = poly.roots(); // [2, 3]
const value = poly.evaluate(2); // 0
const deriv = poly.deriv(); // -5 + 2x
// Complex roots
const allRoots = poly.allRoots(); // includes complex solutions
`$3
typescript
import { line2, bezier2, circle } from '@isopodlabs/maths';// Line from (0,0) to (1,1)
const line = new line2(float2(0, 0), float2(1, 1));
const midpoint = line.evaluate(0.5); // (0.5, 0.5)
// Quadratic Bézier curve
const curve = new bezier2(
float2(0, 0), // start
float2(1, 1), // control
float2(2, 0) // end
);
const point = curve.evaluate(0.5);
const length = curve.lengthTo(1);
// Circle
const circ = new circle(float2(0, 0), 1);
const circumference = circ.lengthTo(1); // 2π
`API Reference
$3
- , float3, float4 - Vector types with swizzling
- float2x2, float2x3, float3x3, etc. - Matrix types
- complex - Complex number type
- polynomial, polynomialN - Polynomial types$3
- normalise(v) - Normalize vector to unit length
- lerp(a, b, t) - Linear interpolation
- project(a, b) - Project vector a onto b
- mid(a, b) - Midpoint between vectors$3
- line - Line segment
- circle - Circle with center and radius
- bezier2, bezier3 - Bézier curves
- polygon - Closed polygonPerformance Notes
- Vectors use object properties (
{x, y, z}`) for optimal performance in V8This project is licensed under the MIT License.