The “B” in B-spline refers to the fact that a segment x.t / may be written in terms of a basis matrix, MS , in a form similar to a Bézier curve. That is,

where G is the geometry matrix [p₀ p₁ p₂ p₃ ] and u(t) is the column vector (1, t, t², t³). In a uniform B-spline, each segment uses the same basis matrix, but the geometry matrix changes. Construct the basis matrix MS for x(t). where G is the geometry matrix [p₀ p₁ p₂ p₃] and u(t) is the column vector (1, t, t², t³). In a uniform B-spline, each segment uses the same basis matrix, but the geometry matrix changes. Construct the basis matrix MS for x(t).

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x(t) = GMsu(t) for 0 ≤ t ≤ 1