Vectors

Point and vector helpers are available in JSX and as named imports. New arrays and points are frozen. Arithmetic preserves NaN/Infinity so sampling can turn invalid results into gaps.

Points and polar coordinates

add2, sub2, mul2, and div2 work component by component. Each operand can be an {x,y} point, a [x,y] pair, or a scalar broadcast to both components. Results are native {x,y} points, ready for Polygon, Points, or Field. Those elements also accept [x,y] inputs directly; see Point values.

add2([1, 2], 3) // {x:4, y:5} mul2([2, 3], [4, 5]) // {x:8, y:15} polar(pi / 2, 2, [1, 1]) // approximately {x:1, y:3} polard(90, [2, 3], [1, 1]) // approximately {x:1, y:4}

polar(angle,radius=1,center=[0,0]) takes radians; polard takes degrees. Radius may be a scalar or separate x/y radii for an ellipse. Center may be a point or pair. Positive angles turn toward positive y; a graph's coordinate mapping determines how that appears on the screen.

addn, subn, muln, and divn operate on numeric arrays of equal length. A length mismatch is an error. Math helpers provides norm and normalize; use normalize(values,2) for a Euclidean unit vector.

Complex values

Complex numbers are [real,imaginary] pairs. addc, subc, mulc, and divc accept either a complex pair or a real scalar and return a pair. conjc conjugates, normc returns magnitude, and argc returns the angle in radians.

mulc([1, 2], [3, 4]) // [-5, 10] divc([3, 4], [1, 2]) // approximately [2.2, -0.4] normc([3, 4]) // 5

Complex division scales its divisor to avoid squaring large components; a zero divisor produces nonfinite results.