SER431 Lecture 05

Advanced Graphics
Bounding Volumes
(201808)

Transcript

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   SER 431
   Advanced Graphics
   Lecture 05: Bounding Volumes (Boxes)
   Javier Gonzalez-Sanchez
   javiergs@asu.edu
   PERALTA 230U
   Office Hours: By appointment
   

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   It could be time to do
   Software Engineering
   

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3. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 3
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   Think about this
   § A class Mesh
   All data is here
   § A class Renderer
   Render a mesh object with and without textures, normals, etc.
   Render a mesh object and visualize its AABB or its normal lines.
   § What about textures?
   § Where do we do collision detection?
   

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   Bounding Volumes (Boxes)
   

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5. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 5
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   Primitives as Bounding Volumes
   § Simple primitives are used as bounding volumes for more complex objects
   § Bounding volumes can be used for approximate intersection tests:
   § If the bounding volumes of two objects do not intersect à the objects
   themselves do not intersect.
   § If the bounding volumes of two objects overlap then maybe there is an
   intersection maybe not
   

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6. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 6
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   Bounding Volumes
   § Axis-aligned Bounding Box (AABB)
   The planes of the box are aligned
   with the world coordinates
   § Object-oriented Bounding Box (OBB)
   The planes are aligned to enclose the
   object as close as possible
   Minimum Volume bounding boxes
   

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7. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 7
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   Bounding Volumes
   § Spheres
   Enclosing sphere
   § Convex Hull
   Closest (convex) fit
   Smallest ratio
   

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8. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 8
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   §Axis-aligned Bounding Box (AABB)
   § An AABB is defined by its minimal and maximal positions in space
   Pmin=(xmin, ymin, zmin),
   Pmax = (xmax, ymax, zmax)
   § Calculate
   Initialize pmin to +infinite or the first vertex
   Initialize pmax to –infinite or the first vertex
   foreach vertex p do {
   if (p.x < pmin.x) then pmin.x = p.x
   if (p.y < pmin.y) then pmin.y = p.y
   if (p.z > pmax.z) then pmax.z = p.z
   }
   

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9. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 9
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   Snippet
   #define MIN2(a,b) (((a) < (b))?(a):(b))
   #define MAX2(a,b) (((a) > (b))?(a):(b))
   // calculate bounding box (AABB)
   void calculateAABB() {
   vector& v = m->dot_vertex;
   if (v.empty()) return;
   boundingMaxPoint = boundingMinPoint = v[0];
   for (unsigned int i = 1; i < v.size(); i++) {
   boundingMinPoint.x = MIN2(boundingMinPoint.x, v[i].x);
   boundingMinPoint.y = MIN2(boundingMinPoint.y, v[i].y);
   boundingMinPoint.z = MIN2(boundingMinPoint.z, v[i].z);
   boundingMaxPoint.x = MAX2(boundingMaxPoint.x, v[i].x);
   boundingMaxPoint.y = MAX2(boundingMaxPoint.y, v[i].y);
   boundingMaxPoint.z = MAX2(boundingMaxPoint.z, v[i].z);
   }
   }
   

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10. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 10
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    Intersection Computations (AABB)
    § Compare min and max in X, Y and Z directions
    § If all of them intersect, then the object intersects
    

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11. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 11
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    Snippet
    // use AABB bounding box to detect intersection
    bool intersect(Mesh* A Mesh* B) {
    Vec3f a1 = A->worldBoundingMinPoint;
    Vec3f b1 = A->worldBoundingMaxPoint;
    Vec3f a2 = B->worldBoundingMinPoint;
    Vec3f b2 = B->worldBoundingMaxPoint;
    int x = 0, y = 0, z = 0;
    if ((a1.x >= a2.x && a1.x <= b2.x) || (b1.x >= a2.x && a1.x <= b2.x) ||
    (a2.x >= a1.x && a2.x <= b1.x) || (b2.x >= a1.x && b2.x <= b1.x))
    x = 1;
    if ((a1.y >= a2.y && a1.y <= b2.y) || (b1.y >= a2.y && a1.y <= b2.y) ||
    (a2.y >= a1.y && a2.y <= b1.y) || (b2.y >= a1.y && b2.y <= b1.y))
    y = 1;
    if ((a1.z >= a2.z && a1.z <= b2.z) || (b1.z >= a2.z && a1.z <= b2.z) ||
    (a2.z >= a1.z && a2.z <= b1.z) || (b2.z >= a1.z && b2.z <= b1.z))
    z = 1;
    if (x == 1 && y == 1 && z == 1) {
    return true;
    }
    else
    return false;
    }
    

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12. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 12
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    Updating AABB
    § Translation invariant
    ✘ Any other kind of movements, box no longer
    remains axis-aligned
    ✘ Needs to be recomputed frame by frame
    § Very simple computation
    

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13. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 13
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    Hierarchical Bounding Volumes
    § At the bottom of such a hierarchy a primitive of one type bounds another
    § For instance, using axis aligned bounding boxes (AABB), to bound triangles.
    The overlap test between two AABBs less expensive than the triangle-
    triangle intersection test.
    

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14. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 14
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    Hierarchical Bounding Volumes
    § Similar to spatial subdivision
    § But for each object Slightly different
    § Union of children may not encompass the parent
    § If does not intersect, do not explore the children
    § If intersects, do bounding volume intersection on children
    § Continue till you get to the triangle-triangle intersection (Very few of them
    needs to be computed)
    

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15. Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 15
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    Homework
    Add Objects to your world
    Calculate AABB
    Draw AABB with lines
    What about drawing the Normal lines?
    

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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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