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This chapter is from the book

This chapter is from the book

Drawing Lines in 3D

The GL_POINTS primitive we have been using thus far is reasonably straightforward; for each vertex specified, it draws a point. The next logical step is to specify two vertices and draw a line between them. This is exactly what the next primitive, GL_LINES, does. The following short section of code draws a single line between two points (0,0,0) and (50,50,50):

glBegin(GL_LINES);
  glVertex3f(0.0f, 0.0f, 0.0f);
  glVertex3f(50.0f, 50.0f, 50.0f);
glEnd();

Note here that two vertices specify a single primitive. For every two vertices specified, a single line is drawn. If you specify an odd number of vertices for GL_LINES, the last vertex is just ignored. Listing 3.4, from the LINES sample program on the CD, shows a more complex sample that draws a series of lines fanned around in a circle. Each point specified in this sample is paired with a point on the opposite side of a circle. The output from this program is shown in Figure 3.6.

Figure 3.6Figure 3.6 Output from the LINES sample program.

Listing 3.4 Code from the Sample Program LINES That Displays a Series of Lines Fanned in a Circle

// Call only once for all remaining points
glBegin(GL_LINES);


// All lines lie in the xy plane.
z = 0.0f;
for(angle = 0.0f; angle <= GL_PI; angle += (GL_PI/20.0f))
  {
  // Top half of the circle
  x = 50.0f*sin(angle);
  y = 50.0f*cos(angle);
  glVertex3f(x, y, z);    // First endpoint of line

  // Bottom half of the circle
  x = 50.0f*sin(angle + GL_PI);
  y = 50.0f*cos(angle + GL_PI);
  glVertex3f(x, y, z);    // Second endpoint of line
  }

// Done drawing points
glEnd();

Line Strips and Loops

The next two OpenGL primitives build on GL_LINES by allowing you to specify a list of vertices through which a line is drawn. When you specify GL_LINE_STRIP, a line is drawn from one vertex to the next in a continuous segment. The following code draws two lines in the xy plane that are specified by three vertices. Figure 3.7 shows an example.

glBegin(GL_LINE_STRIP);
  glVertex3f(0.0f, 0.0f, 0.0f);  // V0
  glVertex3f(50.0f, 50.0f, 0.0f);  // V1
  glVertex3f(50.0f, 100.0f, 0.0f);  // V2
glEnd();

Figure 3.7Figure 3.7 An example of a GL_LINE_STRIP specified by three vertices.

The last line-based primitive is GL_LINE_LOOP. This primitive behaves just like GL_LINE_STRIP, but one final line is drawn between the last vertex specified and the first one specified. This is an easy way to draw a closed-line figure. Figure 3.8 shows a GL_LINE_LOOP drawn using the same vertices as for the GL_LINE_STRIP in Figure 3.7.

Approximating Curves with Straight Lines

The POINTS sample program, shown earlier in Figure 3.3, showed you how to plot points along a spring-shaped path. You might have been tempted to push the points closer and closer together (by setting smaller values for the angle increment) to create a smooth spring-shaped curve instead of the broken points that only approximated the shape. This perfectly valid operation can move quite slowly for larger and more complex curves with thousands of points.

Figure 3.8Figure 3.8 The same vertices from Figure 3.7 used by a GL_LINE_LOOP primitive.

A better way of approximating a curve is to use GL_LINE_STRIP to play connect-the-dots. As the dots move closer together, a smoother curve materializes without your having to specify all those points. Listing 3.5 shows the code from Listing 3.2, with GL_POINTS replaced by GL_LINE_STRIP. The output from this new program, LSTRIPS, is shown in Figure 3.9. As you can see, the approximation of the curve is quite good. You will find this handy technique almost ubiquitous among OpenGL programs.

Figure 3.9Figure 3.9 Output from the LSTRIPS program approximating a smooth curve.

Listing 3.5 Code from the Sample Program LSTRIPS, Demonstrating Line Strips

// Call only once for all remaining points
glBegin(GL_LINE_STRIP);


z = -50.0f;
for(angle = 0.0f; angle <= (2.0f*GL_PI)*3.0f; angle += 0.1f)
  {
  x = 50.0f*sin(angle);
  y = 50.0f*cos(angle);

  // Specify the point and move the z value up a little 
  glVertex3f(x, y, z);
  z += 0.5f;
  }

// Done drawing points
glEnd();

Setting the Line Width

Just as you can set different point sizes, you can also specify various line widths when drawing lines by using the glLineWidth function:

void glLineWidth(GLfloat width);

The glLineWidth function takes a single parameter that specifies the approximate width, in pixels, of the line drawn. Just like point sizes, not all line widths are supported, and you should make sure the line width you want to specify is available. Use the following code to get the range of line widths and the smallest interval between them:

GLfloat sizes[2];  // Store supported line width range
GLfloat step;     // Store supported line width increments


// Get supported line width range and step size
glGetFloatv(GL_LINE_WIDTH_RANGE,sizes);
glGetFloatv(GL_LINE_WIDTH_GRANULARITY,&step);

Here, the sizes array will contain two elements that contain the smallest and largest valid value for glLineWidth. In addition, the variable step will hold the smallest step size allowable between the line widths. The OpenGL specification requires only that one line width, 1.0, be supported. The Microsoft implementation of OpenGL allows for line widths from 0.5 to 10.0, with 0.125 the smallest step size.

Listing 3.6 shows code for a more substantial example of glLineWidth. It's from the program LINESW and draws 10 lines of varying widths. It starts at the bottom of the window at –90 on the y-axis and climbs the y-axis 20 units for each new line. Every time it draws a new line, it increases the line width by 1. Figure 3.10 shows the output for this program.

Figure 3.10Figure 3.10 Demonstration of glLineWidth from the LINESW program.

Listing 3.6 Drawing Lines of Various Widths

// Called to draw scene
void RenderScene(void)
  {
  GLfloat y;        // Storage for varying Y coordinate
  GLfloat fSizes[2];      // Line width range metrics
  GLfloat fCurrSize;      // Save current size

  ...
  ...
  ...

  // Get line size metrics and save the smallest value
  glGetFloatv(GL_LINE_WIDTH_RANGE,fSizes);
  fCurrSize = fSizes[0];

  // Step up y axis 20 units at a time
  for(y = -90.0f; y < 90.0f; y += 20.0f)
    {
    // Set the line width
    glLineWidth(fCurrSize);

    // Draw the line
    glBegin(GL_LINES);
      glVertex2f(-80.0f, y);
      glVertex2f(80.0f, y);
    glEnd();

    // Increase the line width
    fCurrSize += 1.0f;
    }

  ...
  ...
  }

Notice that we used glVertex2f this time instead of glVertex3f to specify the coordinates for the lines. As mentioned, using this technique is only a convenience because we are drawing in the xy plane, with a z value of 0. To see that you are still drawing lines in three dimensions, simply use the arrow keys to spin your lines around. You easily see that all the lines lie on a single plane.

Line Stippling

In addition to changing line widths, you can create lines with a dotted or dashed pattern, called stippling. To use line stippling, you must first enable stippling with a call to

glEnable(GL_LINE_STIPPLE);

Then the function glLineStipple establishes the pattern that the lines use for drawing:

void glLineStipple(GLint factor, GLushort pattern);

Reminder

Any feature or ability that is enabled by a call to glEnable can be disabled by a call to glDisable.

The pattern parameter is a 16-bit value that specifies a pattern to use when drawing the lines. Each bit represents a section of the line segment that is either on or off. By default, each bit corresponds to a single pixel, but the factor parameter serves as a multiplier to increase the width of the pattern. For example, setting factor to 5 causes each bit in the pattern to represent five pixels in a row that are either on or off. Furthermore, bit 0 (the least significant bit) of the pattern is used first to specify the line. Figure 3.11 illustrates a sample bit pattern applied to a line segment.

Why Are These Patterns Backward?

You might wonder why the bit pattern for stippling is used in reverse when drawing the line. Internally, it's much faster for OpenGL to shift this pattern to the left one place each time it needs to get the next mask value. OpenGL was designed for high-performance graphics and frequently employs similar tricks elsewhere.

Figure 3.11Figure 3.11 A stipple pattern is used to construct a line segment.

Listing 3.7 shows a sample of using a stippling pattern that is just a series of alternating on and off bits (0101010101010101). This code is taken from the LSTIPPLE program, which draws 10 lines from the bottom of the window up the y-axis to the top. Each line is stippled with the pattern 0x5555, but for each new line, the pattern multiplier is increased by 1. You can clearly see the effects of the widened stipple pattern in Figure 3.12.

Figure 3.12Figure 3.12 Output from the LSTIPPLE program.

Listing 3.7 Code from LSTIPPLE That Demonstrates the Effect of factor on the Bit Pattern

// Called to draw scene
void RenderScene(void)
  {
  GLfloat y;      // Storage for varying y coordinate
  GLint factor = 1;    // Stippling factor
  GLushort pattern = 0x5555;  // Stipple pattern

...
...

  // Enable Stippling
  glEnable(GL_LINE_STIPPLE);

  // Step up Y axis 20 units at a time
  for(y = -90.0f; y < 90.0f; y += 20.0f)
    {
    // Reset the repeat factor and pattern
    glLineStipple(factor,pattern);

    // Draw the line
    glBegin(GL_LINES);
      glVertex2f(-80.0f, y);
      glVertex2f(80.0f, y);
    glEnd();

    factor++;
    }
  ...
  ...
  }

Just the ability to draw points and lines in 3D gives you a significant set of tools for creating your own 3D masterpiece. I wrote the commercial application shown in Figure 3.13. Note that the OpenGL-rendered map is rendered entirely of solid and stippled line strips.

Figure 3.13Figure 3.13 A 3D map rendered with solid and stippled lines.

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