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Interpolation Vs. Approximation

Interpolation Vs. Approximation. 7. 7. 1. 1. 4. 4. 2. 2. 6. 6. 3. 3. 5. 5. CS 490.006/582.001 Interpolating Values Page 21. De Casteljau Approximation. 4. Quarterpoint between control points 2 and 3. 2. Midpoint between control points 1 and 2.

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Interpolation Vs. Approximation

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  1. Interpolation Vs. Approximation 7 7 1 1 4 4 2 2 6 6 3 3 5 5 CS 490.006/582.001 Interpolating Values Page 21

  2. De Casteljau Approximation 4 Quarterpoint between control points 2 and 3 2 Midpoint between control points 1 and 2 Quarterpoint between first two Quarterpoints Quarterpoint between second two Quarterpoints Midpoint between control points 3 and 4 Bezier point at t=0.25 Midpoint between first two midpoints Bezier point at t=0.5 Quarterpoint between control points 1 and 2 Midpoint between second two midpoints Midpoint between control points 2 and 3 1 Quarterpoint between control points 3 and 4 3 CS 490.006/582.001 Interpolating Values Page 22

  3. Spline Continuity Positional Discontinuity Tangential Discontinuity Curvature Discontinuity CS 490.006/582.001 Interpolating Values Page 23

  4. Arc Length 0.25 0.75 1.0 0.0 0.5 Forward Differencing 1.0 0.0 0.5 Adaptive Subdivision CS 490.006/582.001 Interpolating Values Page 24

  5. Speed Control CS 490.006/582.001 Interpolating Values Page 25

  6. Distance-Time Functions Zero Slope: Smooth Stop Concave Down: Decelerating Distance Negative Slope: Reverse Motion Concave Up: Accelerating Zero Slope: Stall Zero Slope: Smooth Start Positive Slope: Forward Motion Time CS 490.006/582.001 Interpolating Values Page 26

  7. Quaternion Interpolation The resulting arc lengths vary in size, making the rotational transition rates inconsistent. Interpolating rotation may be implemented by performing linear interpolation and projecting points on the interpolated line onto the desired arc. CS 490.006/582.001 Interpolating Values Page 27

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