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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)