OpenGL Curves

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OpenGL Curves Surfaces
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Evaluators
A Bezier curve is a vector-valued function of 1
variable
Where u varies in some domain (say 0,1). A
Bezier surface patch is a vector-valued function
of two variables
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OpenGL Evaluator

• Define the function C( ) or S( )
• Enable it
• Use glEvalCoord1( ) or glEvalCoord2( ) instead of
  glVertex( )
• The curve or surface is used just as any other
  vertices are used.

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Example bezcurve.c
(Note the one I handed out is slightly different
than this one.)
Control Points
Bézier Curve
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bezcurve.c (part 1)
GLfloat ctrlpoints43 -4.0, -4.0,
0.0, -2.0, 4.0, 0.0, 2.0, -4.0,
0.0, 4.0, 4.0, 0.0
void init(void) glClearColor(0.0, 0.0, 0.0,,
0.0) glShadeModel(GL_FLAT)
glMap1f(GL_MAP1_VERTEX_3, 0.0, 1.0, 3, 4,
ctrlpoints00) glEnable(GL_MAP1_VERTEX_3)

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glMap1fd ( )

• GLenum target (see next slide)
• TYPE u1 starting value of u
• TYPE u2 ending value of u
• GLint stride number of single or double
  precision values in each block of storage.
• GLint order degree plus 1 (should agree with
  the number of control points)
• const TYPE points pointer to control points

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glMap1 target parameter

• GL_MAP1_TEXTURE_COORD_2 s,t texture coordinates
• GL_MAP1_TEXTURE_COORD_3 s,t,r texture
  coordinates
• GL_MAP1_TEXTURE_COORD_4 s,t,r,q texture
  coordinates

• GL_MAP1_VERTEX_3 x,y,z vertex coordinates
• GL_MAP1_VERTEX_4 x,y,z,w vertex coordinates
• GL_MAP1_INDEX color index
• GL_MAP1_COLOR_4 R,G,B,A
• GL_MAP1_NORMAL normal coordinates
• GL_MAP1_TEXTURE_COORD_1 s texture coordinate

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glEnable(GL_MAP1_VERTEX_3)

• Enables the one-dimensional evaluator for three
  dimensional vertices.

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bezcurve.c (part 2) display function
void display(void) int i
glClear(GL_COLOR_BUFFER_BIT) glColor3f(1.0,
1.0, 1.0) // set color to white
glBegin(GL_LINE_STRIP) for(i0 ilt30 i)
// loop 31 times glEvalCoord1f((GLfloat)
i/30.0) // call evaluator glEnd( )
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bezcurve.c (part 3)
/ the following code displays the control points
as dots / glPointSize(5.0) glColor3f(1.0, 1.0,
0.0) // set color to yellow glBegin(GL_POINTS)
for(i0 ilt4 i) glVertex3fv(ctrlointsi
0) // Draw a point glEnd( ) glFlush( )
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Bezcurve.c (part 4)

• A reshape function that uses glOrtho for
  orthographic projections and an identity matrix
  for model view.
• A normal main function like all other examples.

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Modification for hand-out

• I changed the color of the bezier curve to red
  and added another bezier curve with different
  parameters.
• Only 4 steps in the evaluator loop.
• (This new curve is drawn in white)
• Note the lack of smoothness.
• Note the same start and end points.

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Additional code
glClear(GL_COLOR_BUFFER_BIT) // clear
screen glColor3f(1.0, 1.0, 1.0) // set
color to white glBegin(GL_LINE_STRIP) //
start a line strip for(i0 ilt4 i)
// loop FIVE times glEvalCoord1f((GLfloat)i/4
.0) // calc a point glEnd( ) glColor3f(1.0,
0.0, 0.0) // set color to
red glBegin(GL_LINE_STRIP) // start a
line strip for(i0 ilt30 i) // loop
31 times glEvalCoord1f((GLfloat)i/30.0) //
calc a point glEnd( )
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4 4.0/4.0 1.0
3 3.0/4.0 0.75
2 2.0/4.0 0.50
15 15.0/30.00.50
1 1.0/4.0 0.25
0 0.0/4.0 0.0
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Calculated Points
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DEMOS

• Bezier /wwwf2003/examples/class
• Curves /wwwf2003/public/curves

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Another way to do even spacing

• void glMapGrid1fd(GLint n, TYPE u1, TYPE u2)
• Void glEvalMesh1(GLenum mode, GLint p1, GLint
  p2) (equivalent to following)

glBegin(GL_POINTS) // or glBegin(GL_LINE_STRIP)
for (ip1 iltp2 i) glEvalCoord1(u1i(u2-
u1)/n) glEnd()
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2D Bezier Surfaces
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Code is bezmeshnolight.c
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bezmesh.c with lighting
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bezsurf.c