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A novel formulation for spatial Pythagorean–hodograph (PH) curves, based on the geometric product of vectors from Clifford algebra, is proposed. Compared to the established quaternion representation, in which a hodograph is generated by a continuous sequence of scalings/rotations of a fixed unit vectorˆn , the new representation corresponds to a sequence of… (More)

A continuous-time formulation of an adaptive critic design (ACD) is investigated. Connections to the discrete case are made, where backpropagation through time (BPTT) and real-time recurrent learning (RTRL) are prevalent. Practical benefits are that this framework fits in well with plant descriptions given by differential equations and that any standard… (More)

In classical photometric stereo, a Lambertian surface is illuminated from multiple distant point light-sources. In the present paper we consider nearby light-sources instead, so that the unknown surface, is illuminated by non-parallel beams of light. In continuous noiseless cases, the recovery of a Lambertian surface from non-distant illuminations, reduces… (More)

This paper studies differences in estimating length (and also trajectory) of an unknown parametric curve γ : [0, 1] → IR n from an ordered collection of data points q i = γ (t i), with either the t i 's known or unknown. For the t i 's uniform (known or unknown) piecewise Lagrange interpolation provides efficient length estimates, but in other cases it may… (More)