SER431 Lecture 10

Advanced Graphics
Environment (Planar shadows)
(201809)

Transcript

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   SER 431
   Advanced Graphics
   Lecture 10: Environment (Planar Shadows)
   Javier Gonzalez-Sanchez
   javiergs@asu.edu
   PERALTA 230U
   Office Hours: By appointment
   

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2. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 1
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   Our Goal
   § Planar Shadow: shadow is projected into the plane of the floor.
   

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3. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 2
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   Planar Shadow
   L = [Lx, Ly, Lz]
   V = [Vx, Vy, Vz]
   P = [Px, Py, Pz]
   N = [Nx, Ny, Nz]
   

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4. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 3
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   Planar Shadow
   § In a 3D space, the line passing through the point L and point V is
   P = L + K *(V - L)
   L = [Lx, Ly, Lz]
   V = [Vx, Vy, Vz]
   P = [Px, Py, Pz]
   N = [Nx, Ny, Nz]
   L = [0.0, 10.0, 5.0]
   P = [20.0, 0.0, -1.0]
   V = [10.0, 5.0, 2.0]
   K=1
   K=2
   

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5. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 4
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   Planar Shadow
   § Having the plain’s normal N and any dot in the plain P,
   dotProduct (N, P) + d = 0 // they are perpendicular
   L = [Lx, Ly, Lz]
   V = [Vx, Vy, Vz]
   P = [Px, Py, Pz]
   N = [0.0, 1.0, 0.0]
   P = [20.0, 0.0, -1.0]
   

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6. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 5
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   Planar Shadow
   § Having the plain’s normal N and any dot in the plain P,
   dotProduct (N, P) + d = 0 // they are perpendicular
   n • a – 32.5 = 0
   n • c – 32.5 = 0
   n • b – 32.5 = 0
   y = - x + 5
   N = [6.5,6.5,z]
   b = [5,0,z]
   a=[0,5,z]
   c = [2.5,2.5,z]
   

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7. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 6
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   Planar Shadow
   § Line passing through L and V:
   P = L + K * (V - L)
   § Equation for a plane:
   N ● P + d = 0
   § K can be solved as:
   K = - (d + N ● L) / (N ●(V-L)
   § Then
   P = L + ((d + N ● L) / (N ●(V - L))(V - L)
   § And, simplifying,
   

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8. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 7
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   The Shadow Matrix
   dot(N,L)–Lx Nx – Ly Nx – Lz Nx – Lw Nx
   – Lx Ny dot(N,L)–Ly Ny – Lz Ny – Lw Ny
   – Lx Nz – Ly Nz dot(N,L)–Lz Nz – Lw Nz
   – Lx Nw – Ly Nw – Lz Nw – Lw Nw
   Shadow Matrix Vector
   Vx
   Vy
   Vz
   1
   

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9. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 8
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   The Shadow Matrix
   dot(N,L)–Lx Nx – Ly Nx – Lz Nx – Lw Nx
   – Lx Ny dot(N,L)–Ly Ny – Lz Ny – Lw Ny
   – Lx Nz – Ly Nz dot(N,L)–Lz Nz – Lw Nz
   – Lx Nw – Ly Nw – Lz Nw – Lw Nw
   Shadow Matrix
   Scale
   Translate
   Rotate
   

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10. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 9
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    The Shadow Matrix
    

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    Source Code
    

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12. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 11
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    Planar Shadows
    

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    main()
    void main(int argc, char* argv[]) {
    // as usual here
    glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH | GLUT_STENCIL);
    // as usual here
    }
    

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14. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 13
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    init()
    void init() {
    // as usual here
    glClearStencil(0);
    // floor vertex
    dot_vertex_floor.push_back(Vec3(-2000.0, 0.0, 2000.0));
    dot_vertex_floor.push_back(Vec3(2000.0, 0.0, 2000.0));
    dot_vertex_floor.push_back(Vec3(2000.0, 0.0, -2000.0));
    dot_vertex_floor.push_back(Vec3(-2000.0, 0.0, -2000.0));
    calculate_floor_normal(&floor_normal, dot_vertex_floor );
    // light
    glEnable(GL_LIGHT0);
    glEnable(GL_LIGHTING);
    }
    

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15. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 14
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    display()
    void display(void) {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT | GL_STENCIL_BUFFER_BIT);
    // light source position
    light_position[0] = 500 * cos(lightAngle);
    light_position[1] = lightHeight;
    light_position[2] = 500 * sin(lightAngle);
    light_position[3] = 0.0; // directional light
    // light moving
    lightAngle += 0.0005;
    // Calculate Shadow matrix
    shadowMatrix(shadow_matrix, floor_normal, light_position);
    

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16. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 15
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    // projection and view
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    glViewport(0, 0, width, height);
    gluPerspective(40.0, ratio, 1, 1000);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    // lookAt
    gluLookAt(0.0f, 40.0f, 320.0, 0.0f, 1.0f, -1.0f, 0.0f, 1.0f, 0.0f);
    // camera
    glScalef(scale, scale, scale);
    glRotatef(x_angle, 1.0f, 0.0f, 0.0f);
    glRotatef(y_angle, 0.0f, 1.0f, 0.0f);
    glTranslatef(0.0f, 0.0f, 0.0f);
    

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17. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 16
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    // draw
    glPushMatrix();
    glLightfv(GL_LIGHT0, GL_POSITION, light_position); // light position
    // shadows
    if (renderShadow) {
    glEnable(GL_STENCIL_TEST);
    glStencilFunc(GL_ALWAYS, 1, 0xFFFFFFFF);
    glStencilOp(GL_REPLACE, GL_REPLACE, GL_REPLACE);
    }
    // draw floor
    glEnable(GL_BLEND); glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
    glColor4f(1.0, 1.0, 1.0, 0.3);
    glPushMatrix();
    glDisable(GL_LIGHTING);
    glTranslatef(-900, 0, -900); glCallList(display1);
    glEnable(GL_LIGHTING);
    glPopMatrix();
    glDisable(GL_BLEND);
    

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18. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 17
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    if (renderShadow) {
    glStencilFunc(GL_EQUAL, 1, 0xFFFFFFFF);
    glStencilOp(GL_KEEP, GL_KEEP, GL_KEEP);
    // Render 50% black shadow color on top of the floor
    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
    glDisable(GL_LIGHTING); /* Force the 50% black. */
    glColor4f(0.0, 0.0, 0.0, 0.5);
    glPushMatrix();
    glMultMatrixf((GLfloat *)shadow_matrix);
    glDisable(GL_DEPTH_TEST);
    // shadows for box 1, 2, 3
    glEnable(GL_DEPTH_TEST);
    glPopMatrix();
    glDisable(GL_BLEND);
    glEnable(GL_LIGHTING);
    glDisable(GL_STENCIL_TEST);
    }
    

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19. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 18
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    // box 1
    glPushMatrix();
    glCallList(display2);
    glPopMatrix();
    // box 2
    glPushMatrix();
    glTranslatef(200, 0, 0); glCallList(display3);
    glPopMatrix();
    // box 3
    glPushMatrix();
    glTranslatef(-200, 0, 0); glCallList(display4);
    glPopMatrix();
    // draw the light arrow
    drawLightArrow();
    glPopMatrix();
    glutSwapBuffers();
    }
    

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    Double Blending
    

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21. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 20
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    Avoid Double Blending
    glStencilFunc(GL_ALWAYS, 1, 0xFFFFFFFF);
    glStencilOp(GL_REPLACE, GL_REPLACE, GL_REPLACE);
    // code here
    glStencilFunc(GL_EQUAL, 1, 0xFFFFFFFF);
    glStencilOp(GL_KEEP, GL_KEEP, GL_KEEP);
    

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22. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 21
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    Avoid Double Blending
    glStencilFunc(GL_ALWAYS, 1, 0xFFFFFFFF);
    glStencilOp(GL_REPLACE, GL_REPLACE, GL_REPLACE);
    // code here
    glStencilFunc(GL_EQUAL, 1, 0xFFFFFFFF);
    glStencilOp(GL_ZERO, GL_ZERO, GL_ZERO);
    

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    Test Yourselves
    

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24. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 23
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    Test Yourselves
    § Change renderShadow from 1 to 0
    § Change lightHeight from 100 to 1000 and 10
    § Change light type from directional (0) to positional light
    § Verify:
    § glStencilOp(GL_KEEP, GL_KEEP, GL_KEEP);
    § glStencilOp(GL_ZERO, GL_ZERO, GL_ZERO);
    § Make the light rotate like a Sun (around z or x axis)
    § Put together shadows and reflection.
    § Replace a box with an OBJ object.
    

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    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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