Lecture2/1: Perspective Projection and Wireframe Depth Cue Rendering

Download.

Click here to download source code of this lecture.

Click here to download an obj file of Stanford bunny model.

Programming

• Define a simple Point structure; you can put just before Canvas class, or into a new file named Point.h. The Point struct (a struct is a class of public access) only has a constructor and three data members (x,y and z component of the point).

  You should also type-define Point struct as Vertex and Vector type.

• Add a data member

        double eye_at;
  

  to Canvas class. Now you have to image the Canvas in a 3D space setting. The canvas is center at z = 0, coincident with xy plane, and with size along x direction of hReso, and that of y direction vReso. The eye is at position (0, 0, eye_at), where eye_at is a positive value, and looking along negative z direction. The eye and the (rectangle) canvas forms a (infinite) pyramid, which is called viewing volume.

  Add this line to the init() member function,

        eye_at = Reso / 2;
  

  so the the eye has a default angle span(called field of view, fov) of 90 degreen along x direction.

  If you want user control on eye position and therefore fov, you can write the appropriate access member function(s).

• Add a private data member and function member.

         Point perspectiveProjection(Point const&); 
  

  This private member function computes the projected x and y values which, together with the unchanged z component, is returned as a Point object. The unchanged z value is used for z-buffer algorithm later.

• Now change the member function,

        void WireTriangle(int x1, int y1, RGB const& col1, int x2, int y2, RGB const& col2, int x3, int y3, RGB const& col3);
  

  into

        void WireTriangle(Point const& P1, RGB const& col1, Point const& P2, RGB const& col2, Point const& P3, RGB const& col3);
  

  You have to do the projections of all three points, and then proceed as usual (simply ignore the z-component for now).

• A little debugging. Our old code in ScanLineSegment() has a bug at this line,

        swap ( (RGB&)col1, (RGB&)col2 );
  

  We should make loca copies

        RGB c1(col1), c2(col2);
  

  and then do the swap,

        swap (c1, c2);
  

  and thereafter, every reference to col1(col2) should be replaced by c1(c2)

• Take a look at TriangleFace and TriangleMesh structs. They are used to read an obj file of 3D model. The constructor is very simple, and I will update it later to make it more robust.

• Write a class called BBox, meaning bounding box. Every TriangleMesh object should have a BBox object as its data member, which tells the axis aligned bounding box of the model. Here is a template of the BBox class,

        namespace columbia 
        {
           struct BBox
           {
                  Point min, max;
                  // A Constructor: create a bounding box from two points of the box, one is lowerleft corner, the other upperright corner..
                  // A Constructor: create a bounding box from a TriangleMesh object. This bascially creates a bbox for the model.
          };
       }
  

• Add a BBox object member to TriangleMesh class. You also need to add some code in the constructor, to initialize the BBox object.

• Use to the BBox object. BBox is one of the most used data structure in computer graphics. For our course it is used to,
  • Translate the model to the center of the secene.
  • Scale it so it fits into our viewing volume.
  • Use the z value of each vertex to do depth cueing.
  • Approximate collision detection using the bounding box instead of the actual model.

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