Project 4

1
Project 4

• Relief Map
• Fri, Oct 24, 2003
• Due Fri, Oct 31, 2003

2
Relief Map

• Read the handout.
• Download the files.
• ReliefMap.cpp.
• point3.h.
• vector3.h.
• ThePriest.topo.
• Run ReliefMap.exe.

3
Relief Map

• The primary purpose of this project is to compute
  normals to a mesh so that the lighting models
  creates the right effects.
• A secondary purpose is to learn how to render the
  mesh.

4
The Grid

• The grid of terrain points extends from a
  beginning to an ending longitude and from a
  beginning to an ending latitude.
• Each grid point is represented by three
  coordinates, expressed in miles.
• x the distance from the west edge.
• y the elevation.
• z the distance from the north edge.

5
The Grid

• You may render the grid as a grid of rectangles.

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The Grid

• Or you may render it as a grid of triangles.

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The Topo Structure

• The data from the file ThePriest.topo is read
  into a Topo structure.

typedef struct int lngCnt int latCnt
Point3 pt Vector3 norm double
min double max Topo
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The Topo Structure

• lngCnt (longitude count) is the number of grid
  points in an east-west direction.
• latCnt (latitude count) is the number of grid
  points in a north-south direction.
• pt is a pointer to a 2-dimensional array of
  Point3 objects.
• norm is a pointer to 2-dimensional array of
  Vector3 objects.
• min and max are the minimum and maximum
  elevations in the file.

9
The Project

• Your job is to compute the normals at the grid
  points and to render the surface.
• This will involve writing parts or all of three
  functions
• setNormals()
• drawTerrain()
• computeNormal()

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The setNormals() Function

• The setNormals() function should compute a unit
  normal for each grid point by calling on
  computeNormal().
• The direction of the normal should represent the
  general slope of the land.
• The normals should be stored in the Topo
  structure as they are computed.

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Computing Normals

• To compute normals, we consider three cases.
• Interior grid points 4 neighbors.
• Edge grid points 3 neighbors.
• Corner grid points 2 neighbors.

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Computing Interior Normals

• The four neighbors are north, south, east, and
  west.

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Computing Interior Normals

• We may form two vectors and take their cross
  product.

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Computing Edge Normals

• For edge points, use a similar method, but use
  the grid point itself as one of the four points.

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Computing Edge Normals

• For edge points, use a similar method, but use
  the grid point itself as one of the four points.

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Computing Corner Normals

• For corner points, again use a similar idea, but
  based on only three points.

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Computing Corner Normals

• For corner points, again use a similar idea, but
  based on only three points.

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Newells Algorithm

• The textbook, on page 292, discusses Newells
  Algorithm for computing a normal to a (possibly)
  non-planar polygon.
• It is based on the concept of the cross product,
  but it is more efficient.
• You may use Newells algorithm instead of
  computing cross products.

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Newells Algorithm for Quadrilaterals

• Let the vertices be (x0, y0, z0), (x1, y1, z1),
  (x2, y2, z2), (x3, y3, z3).
• Then the normal v (vx, vy, vz) is computed as
• vx (y0 y1)(z0 z1) (y1 y2)(z1 z2)
• (y2 y3)(z2 z3) (y3 y0)(z3 z0).
• vy (z0 z1)(x0 x1) (z1 z2)(x1 x2)
• (z2 z3)(x2 x3) (z3 z0)(x3 x0).
• vz (x0 x1)(y0 y1) (x1 x2)(y1 y2)
• (x2 x3)(y2 y3) (x3 x0)(y3 y0).

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Newells Algorithm for Triangles

• Let the vertices be (x0, y0, z0), (x1, y1, z1),
  (x2, y2, z2).
• Then the normal v (vx, vy, vz) is computed as
• vx (y0 y1)(z0 z1) (y1 y2)(z1 z2)
• (y2 y0)(z2 z0).
• vy (z0 z1)(x0 x1) (z1 z2)(x1 x2)
• (z2 z0)(x2 x0).
• vz (x0 x1)(y0 y1) (x1 x2)(y1 y2)
• (x2 x0)(y2 y0).

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Quadrilaterals vs. Triangles

• If you use Newells algorithm, you may write a
  separate function to deal with triangles.
• Or you may use the function designed for
  quadrilaterals by repeating the first point as
  the fourth point.
• The results will be the same.

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The drawTerrain() Function

• The drawTerrain() function will draw render the
  grid with each polygon properly colored.
• To draw a vertex, we must first
• Color the vertex.
• Give it a normal vector.

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The drawTerrain() Function

• This uses the functions
• glColor().
• glNormal().

glBegin(GL_POLYGON) glColor3f(1.0, 0.0,
0.0) // Red glNormal3f(0.0, 1.0, 0.0) //
Up glVertex3f(1.0, 2.0, 3.0) //
Coordinates glEnd()
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The setColor() Function

• The setColor() function is provided, but you
  should understand how it works.
• The elevation of the point is compared to each
  elevation that was read from the file, starting
  with the smallest.
• As soon as a higher elevation is found, the
  corresponding color is set.
• If no higher elevation is found, then the last
  color is set.