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(x0, y0)

Curva Bezier 2o. Orden. (x1, y1). (x2, y2). (x0, y0). Curva Bezier 2o. Orden. 1 -2 1 x 0 y 0 (x’,y’) = (t 2 t 1 ) -2 2 0 x 1 y 1 1 0 0 x 2 y 2. Curva Bezier 3er Orden. (x1, y1). (x2, y2). (x0, y0). (x3, y3).

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(x0, y0)

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  1. Curva Bezier 2o. Orden (x1, y1) (x2, y2) (x0, y0) Mario H Tiburcio Z

  2. Curva Bezier 2o. Orden 1 -2 1 x0 y0 (x’,y’) = (t2 t 1) -2 2 0 x1 y1 1 0 0 x2 y2 Mario H Tiburcio Z

  3. Curva Bezier 3er Orden (x1, y1) (x2, y2) (x0, y0) (x3, y3) Mario H Tiburcio Z

  4. Curva Bezier 3er Orden -1 3 -3 1 x0 y0 (x’,y’) = (t3 t2 t 1) 3 -6 3 0 x1 y1 -3 3 0 0 x2 y2 1 0 0 0 x3 y3 Mario H Tiburcio Z

  5. Parche de Bezier t=0 s=1 t=1 s=1 s t t=0 s=0 t=1 s=0 Mario H Tiburcio Z

  6. Parche de Bezier P32 P31 P33 P30 P22 P21 P20 P23 P11 P12 P10 P01 P13 P02 P03 P00 Mario H Tiburcio Z

  7. Puntos de control del parche P00=(X00 Y00 Z00) P20=( X20 Y20 Z20) P01=(X01 Y01 Z01) P21=( X21 Y21 Z21) P02=( X02 Y02 Z02) P22=( X22 Y22 Z22) P03=( X03 Y03 Z03) P23=( X23 Y23 Z23) P10=( X10 Y10 Z10) P30=( X30 Y30 Z30) P11=( X11 Y11 Z11) P31=( X31 Y31 Z31) P12=( X12 Y12 Z12) P32=( X32 Y32 Z32) P13=( X13 Y13 Z13) P33=( X33 Y33 Z33) Mario H Tiburcio Z

  8. Ecuaciones paramétrica para calcular x,y,z t3 x(s,t) = (s3 s2 s 1) x M x B x MTx t2 t 1 Mario H Tiburcio Z

  9. t3 y(s,t) = (s3 s2 s 1) x M x B x MTx t2 t 1 t3 z(s,t) = (s3 s2 s 1) x M x B x MTx t2 t 1 Mario H Tiburcio Z

  10. Matriz M -1 3 -3 1 M = MT = 3 -6 3 0 -3 3 0 0 1 0 0 0 Mario H Tiburcio Z

  11. Matriz B de valores X X00 X01 X02 X03 B = X10 X11 X12 X13 X20 X21 X22 X23 X30 X31 X32 X33 Mario H Tiburcio Z

  12. Matriz B de valores Y Y00 Y01 Y02 Y03 B = Y10 Y11 Y12 Y13 Y20 Y21 Y22 Y23 Y30 Y31 Y32 Y33 Mario H Tiburcio Z

  13. Matriz B de valores Z Z00 Z01 Z02 Z03 B = Z10 Z11 Z12 Z13 Z20 Z21 Z22 Z23 Z30 Z31 Z32 Z33 Mario H Tiburcio Z

  14. Demostración Mario H Tiburcio Z

  15. Mario H Tiburcio Z

  16. Mario H Tiburcio Z

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  18. Mario H Tiburcio Z

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