SER431 Lecture 20

Advanced Graphics
NURBS II
(201811)

Transcript

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   SER 431
   Advanced Graphics
   Lecture 20: Non-Uniform Rational Basis Splines II
   Javier Gonzalez-Sanchez
   javiergs@asu.edu
   PERALTA 230U
   Office Hours: By appointment
   

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   Surfaces using OpenGL Support
   Solid Shape with Materials and Light
   

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3. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 2
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   Screenshot
   https://github.com/javiergs/SER431/blob/master/Lecture19/nurbs_surface_grid.cpp
   https://github.com/javiergs/SER431/blob/master/Lecture19/nurbs_surface_solid.cpp
   

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4. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 3
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   Code
   // control points
   GLfloat ctlpoints[4][4][3] = {
   { { 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } },
   { { 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } },
   { { 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } },
   { { 20, 0, -10 },{ 0, 0, -10 },{ -5, 0, -10 },{ -10, 0, -10 } }
   };
   GLfloat knots[8] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0 };
   GLUnurbsObj *theNurb;
   

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5. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 4
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   Code
   // init
   void init(void) {
   // Materials and Light
   GLfloat mat_diffuse[] = { 1.0f, 0.5f, 0.31f, 1. };
   GLfloat mat_specular[] = { 0.5f, 0.5f, 0.5f, 1. };
   GLfloat mat_ambient[] = { 1.0f, 0.5f, 0.31f, 1. };
   GLfloat mat_shininess[] = { 100.0 };
   glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, mat_ambient);
   glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, mat_diffuse);
   glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_specular);
   glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, mat_shininess);
   glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glEnable(GL_DEPTH_TEST);
   glEnable(GL_AUTO_NORMAL);
   glEnable(GL_NORMALIZE);
   theNurb = gluNewNurbsRenderer();
   gluNurbsProperty(theNurb, GLU_SAMPLING_TOLERANCE, 25.0);
   gluNurbsProperty(theNurb, GLU_DISPLAY_MODE, GLU_FILL);
   }
   

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6. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 5
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   // display
   void display(void) {
   // camera and others configurations here...
   // NURBS
   glColor3f(0, 1, 0);
   gluBeginSurface(theNurb);
   gluNurbsSurface(theNurb,
   8, knots, 8, knots, // knots u and v
   4 * 3, 3, // offset u and v
   &ctlpoints[0][0][0],
   4, 4, // function degree u and v
   GL_MAP2_VERTEX_3);
   gluEndSurface(theNurb);
   // more ...
   }
   

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7. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 6
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   Numbers to be considered
   // V_size curves with U_size control points each
   // V_size + ORDER knots per curve and
   // U_size + ORDER knots per inter-curve connection
   // offsets are V_size*3 and 3
   // cubic equations ORDER = 4
   GLfloat ctlpoints[U_size][V_size][3] = { … };
   GLfloat vknots [V_size + ORDER] = { …};
   GLfloat uknots [U_size + ORDER] = { …}
   gluNurbsSurface(theNurb,U_size + ORDER, uknots,
   V_size + ORDER, vknots,
   V_size * 3, 3,
   &ctlpoints[0][0][0],
   ORDER, ORDER,
   GL_MAP2_VERTEX_3);
   

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8. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 7
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   Screenshot
   6 curves
   6 control points each
   5 curves
   6 control points each
   4 curves
   6 control points each
   

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9. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 8
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   6 curves x 6 control points per curve
   const int V_size = 6;
   const int U_size = 6; // curves in blue color
   const int ORDER = 4;
   GLfloat ctlpoints[U_size][V_size][3] = {
   { { 25, 5, 15 } ,{ 20, 5, 15 },{ 0, 0, 15 },{ -5, 0, 15 },{ -10, 5, 15 } ,{ -15, 5, 15 } },
   { { 25, 5, 10 } ,{ 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } ,{ -15, 5, 10 } },
   { { 25, 0, 5 } ,{ 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } ,{ -15, 0, 5 } },
   { { 25, 0, -5 } ,{ 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } ,{ -15, 0, -5 } },
   { { 25, 5, -10 } ,{ 20, 0, -10 },{ 0, 0, -10 },{ -5, 0, -10 },{ -10, 0, -10 } ,{ -15, 5, -10 } },
   { { 25, 5, -15 } ,{ 20, 5, -15 },{ 0, 0, -15 },{ -5, 0, -15 },{ -10, 5, -15 } ,{ -15, 5, -15 } }
   };
   GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 3.0, 5.0, 5.0, 5.0, 5.0 };
   GLfloat vknots[V_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 3.0, 5.0, 5.0, 5.0, 5.0 };
   gluBeginSurface(theNurb);
   gluNurbsSurface(theNurb,
   U_size + ORDER, uknots, V_size + ORDER, vknots,
   V_size * 3, 3,
   &ctlpoints[0][0][0],
   ORDER, ORDER, GL_MAP2_VERTEX_3);
   gluEndSurface(theNurb);
   

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10. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 9
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    5 curves x 6 control points per curve
    const int V_size = 6;
    const int U_size = 5; // curves in blue color
    const int ORDER = 4;
    GLfloat ctlpoints[U_size][V_size][3] = {
    { { 25, 5, 15 } ,{ 20, 5, 15 },{ 0, 0, 15 },{ -5, 0, 15 },{ -10, 5, 15 } ,{ -15, 5, 15 } },
    { { 25, 5, 10 } ,{ 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } ,{ -15, 5, 10 } },
    { { 25, 0, 5 } ,{ 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } ,{ -15, 0, 5 } },
    { { 25, 0, -5 } ,{ 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } ,{ -15, 0, -5 } },
    { { 25, 5, -10 } ,{ 20, 0, -10 },{ 0, 0, -10 },{ -5, 0, -10 },{ -10, 0, -10 } ,{ -15, 5, -10 } }
    };
    GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 4.0, 4.0, 4.0, 4.0};
    GLfloat vknots[V_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 3.0, 5.0, 5.0, 5.0, 5.0 };
    gluBeginSurface(theNurb);
    gluNurbsSurface(theNurb,
    U_size + ORDER, uknots, V_size + ORDER, vknots,
    V_size * 3, 3,
    &ctlpoints[0][0][0],
    ORDER, ORDER, GL_MAP2_VERTEX_3);
    gluEndSurface(theNurb);
    

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11. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 10
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    4 curves x 6 control points per curve
    const int V_size = 6;
    const int U_size = 4; // curves in blue color
    const int ORDER = 4;
    GLfloat ctlpoints[U_size][V_size][3] = {
    { { 25, 5, 15 } ,{ 20, 5, 15 },{ 0, 0, 15 },{ -5, 0, 15 },{ -10, 5, 15 } ,{ -15, 5, 15 } },
    { { 25, 5, 10 } ,{ 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } ,{ -15, 5, 10 } },
    { { 25, 0, 5 } ,{ 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } ,{ -15, 0, 5 } },
    { { 25, 0, -5 } ,{ 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } ,{ -15, 0, -5 } }
    };
    GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0};
    GLfloat vknots[V_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 3.0, 5.0, 5.0, 5.0, 5.0 };
    gluBeginSurface(theNurb);
    gluNurbsSurface(theNurb,
    U_size + ORDER, uknots, V_size + ORDER, vknots,
    V_size * 3, 3,
    &ctlpoints[0][0][0],
    ORDER, ORDER, GL_MAP2_VERTEX_3);
    gluEndSurface(theNurb);
    

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12. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 11
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    Test Yourselves
    What about 3?
    

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13. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 12
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    Test Yourselves
    What about 3?
    We need at least 4 using Cubic B-splines
    

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14. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 13
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    Screenshot
    4 curves
    6 control points each
    4 curves
    5 control points each
    4 curves
    4 control points each
    

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15. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 14
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    4 curves x 6 control points per curve
    const int V_size = 6;
    const int U_size = 4; // curves in blue color
    const int ORDER = 4;
    GLfloat ctlpoints[U_size][V_size][3] = {
    { { 25, 5, 15 } ,{ 20, 5, 15 },{ 0, 0, 15 },{ -5, 0, 15 },{ -10, 5, 15 } ,{ -15, 5, 15 } },
    { { 25, 5, 10 } ,{ 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } ,{ -15, 5, 10 } },
    { { 25, 0, 5 } ,{ 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } ,{ -15, 0, 5 } },
    { { 25, 0, -5 } ,{ 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } ,{ -15, 0, -5 } }
    };
    GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0};
    GLfloat vknots[V_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 3.0, 5.0, 5.0, 5.0, 5.0 };
    gluBeginSurface(theNurb);
    gluNurbsSurface(theNurb,
    U_size + ORDER, uknots, V_size + ORDER, vknots,
    V_size * 3, 3,
    &ctlpoints[0][0][0],
    ORDER, ORDER, GL_MAP2_VERTEX_3);
    gluEndSurface(theNurb);
    

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16. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 15
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    4 curves x 5 control points per curve
    const int V_size = 5;
    const int U_size = 4; // curves in blue color
    const int ORDER = 4;
    GLfloat ctlpoints[U_size][V_size][3] = {
    { { 20, 5, 15 },{ 0, 0, 15 },{ -5, 0, 15 },{ -10, 5, 15 } ,{ -15, 5, 15 } },
    { { 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } ,{ -15, 5, 10 } },
    { { 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } ,{ -15, 0, 5 } },
    { { 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } ,{ -15, 0, -5 } }
    };
    GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0};
    GLfloat vknots[V_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 1.0, 4.0, 4.0, 4.0, 4.0 };
    gluBeginSurface(theNurb);
    gluNurbsSurface(theNurb,
    U_size + ORDER, uknots, V_size + ORDER, vknots,
    V_size * 3, 3,
    &ctlpoints[0][0][0],
    ORDER, ORDER, GL_MAP2_VERTEX_3);
    gluEndSurface(theNurb);
    

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17. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 16
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    4 curves x 4 control points per curve
    const int V_size = 4;
    const int U_size = 4; // curves in blue color
    const int ORDER = 4;
    GLfloat ctlpoints[U_size][V_size][3] = {
    { { 0, 0, 15 },{ -5, 0, 15 },{ -10, 5, 15 } ,{ -15, 5, 15 } },
    { { 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } ,{ -15, 5, 10 } },
    { { 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } ,{ -15, 0, 5 } },
    { { 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } ,{ -15, 0, -5 } }
    };
    GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0};
    GLfloat vknots[V_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0};
    gluBeginSurface(theNurb);
    gluNurbsSurface(theNurb,
    U_size + ORDER, uknots, V_size + ORDER, vknots,
    V_size * 3, 3,
    &ctlpoints[0][0][0],
    ORDER, ORDER, GL_MAP2_VERTEX_3);
    gluEndSurface(theNurb);
    

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18. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 17
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    Note
    § GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 2.0, 4.0, 4.0, 4.0, 3.0};
    § GLfloat uknots[U_size + ORDER] = { 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0, 1.0};
    

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19. jgs
    Quiz 06 NURBS
    

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20. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 19
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    Problem A
    https://github.com/javiergs/SER431/blob/master/Lecture20/nurbs_surface_controlled.cpp
    

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21. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 20
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    Problem B
    https://github.com/javiergs/SER431/blob/master/Lecture20/nurbs_surface_controlled.cpp
    * There are 7
    squares (i.e., 7
    curves)in blue.
    * You need 8 control
    points per square;
    BUT since you want
    to close the curve.
    You may should need
    to add the first one
    again. Thus 8 + 1
    

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22. jgs
    SER431 Advanced Graphics
    Javier Gonzalez-Sanchez
    javiergs@asu.edu
    Fall 2018
    Disclaimer. These slides can only be used as study material for the class SER431 at ASU. They cannot be
    distributed or used for another purpose.
    

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