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This chapter is from the book

Displaying Points, Lines, and Polygons

By default, a point is drawn as a single pixel on the screen, a line is drawn solid and 1 pixel wide, and polygons are drawn solidly filled in. The following paragraphs discuss the details of how to change these default display modes.

Point Details

To control the size of a rendered point, use glPointSize() and supply the desired size in pixels as the argument.

The actual collection of pixels on the screen that are drawn for various point widths depends on whether antialiasing is enabled. (Antialiasing is a technique for smoothing points and lines as they’re rendered; see “Antialiasing” and “Point Parameters” in Chapter 6 for more detail.) If antialiasing is disabled (the default), fractional widths are rounded to integer widths, and a screen-aligned square region of pixels is drawn. Thus, if the width is 1.0, the square is 1 pixel by 1 pixel; if the width is 2.0, the square is 2 pixels by 2 pixels; and so on.

With antialiasing or multisampling enabled, a circular group of pixels is drawn, and the pixels on the boundaries are typically drawn at less than full intensity to give the edge a smoother appearance. In this mode, noninteger widths aren’t rounded.

Most OpenGL implementations support very large point sizes. You can query the minimum and maximum sized for aliased points by using GL_ALIASED_POINT_SIZE_RANGE with glGetFloatv(). Likewise, you can obtain the range of supported sizes for antialiased points by passing GL_SMOOTH_POINT_SIZE_RANGE to glGetFloatv(). The sizes of supported antialiased points are evenly spaced between the minimum and maximum sizes for the range. Calling glGetFloatv() with the parameter GL_SMOOTH_POINT_SIZE_GRANULARITY will return how accurately a given antialiased point size is supported. For example, if you request glPointSize(2.37) and the granularity returned is 0.1, then the point size is rounded to 2.4.

Line Details

With OpenGL, you can specify lines with different widths and lines that are stippled in various ways—dotted, dashed, drawn with alternating dots and dashes, and so on.

Wide Lines

The actual rendering of lines is affected if either antialiasing or multisampling is enabled. (See “Antialiasing Points or Lines” on page 269 and “Antialiasing Geometric Primitives with Multisampling” on page 275.) Without antialiasing, widths of 1, 2, and 3 draw lines 1, 2, and 3 pixels wide. With antialiasing enabled, noninteger line widths are possible, and pixels on the boundaries are typically drawn at less than full intensity. As with point sizes, a particular OpenGL implementation might limit the width of non-antialiased lines to its maximum antialiased line width, rounded to the nearest integer value. You can obtain the range of supported aliased line widths by using GL_ALIASED_LINE_WIDTH_RANGE with glGetFloatv(). To determine the supported minimum and maximum sizes of antialiased line widths, and what granularity your implementation supports, call glGetFloatv(), with GL_SMOOTH_LINE_WIDTH_RANGE and GL_SMOOTH_LINE_WIDTH_GRANULARITY.

Advanced

With non-antialiased wide lines, the line width isn’t measured perpendicular to the line. Instead, it’s measured in the y-direction if the absolute value of the slope is less than 1.0; otherwise, it’s measured in the x-direction. The rendering of an antialiased line is exactly equivalent to the rendering of a filled rectangle of the given width, centered on the exact line.

Stippled Lines

To make stippled (dotted or dashed) lines, you use the command glLineStipple() to define the stipple pattern, and then you enable line stippling with glEnable().

glLineStipple(1, 0x3F07);
glEnable(GL_LINE_STIPPLE);

With the preceding example and the pattern 0x3F07 (which translates to 0011111100000111 in binary), a line would be drawn with 3 pixels on, then 5 off, 6 on, and 2 off. (If this seems backward, remember that the low-order bit is used first.) If factor had been 2, the pattern would have been elongated: 6 pixels on, 10 off, 12 on, and 4 off. Figure 2-8 shows lines drawn with different patterns and repeat factors. If you don’t enable line stippling, drawing proceeds as if pattern were 0xFFFF and factor were 1. (Use glDisable() with GL_LINE_STIPPLE to disable stippling.) Note that stippling can be used in combination with wide lines to produce wide stippled lines.

Figure 2-8

Figure 2-8 Stippled Lines

One way to think of the stippling is that as the line is being drawn, the pattern is shifted by 1 bit each time a pixel is drawn (or factor pixels are drawn, if factor isn’t 1). When a series of connected line segments is drawn between a single glBegin() and glEnd(), the pattern continues to shift as one segment turns into the next. This way, a stippling pattern continues across a series of connected line segments. When glEnd() is executed, the pattern is reset, and if more lines are drawn before stippling is disabled the stippling restarts at the beginning of the pattern. If you’re drawing lines with GL_LINES, the pattern resets for each independent line.

Example 2-5 illustrates the results of drawing with a couple of different stipple patterns and line widths. It also illustrates what happens if the lines are drawn as a series of individual segments instead of a single connected line strip. The results of running the program appear in Figure 2-9.

Figure 2-9

Figure 2-9 Wide Stippled Lines

Example 2-5. Line Stipple Patterns: lines.c

#define drawOneLine(x1,y1,x2,y2)  glBegin(GL_LINES);     glVertex2f((x1),(y1)); glVertex2f((x2),(y2)); glEnd();

void init(void)
{
   glClearColor(0.0, 0.0, 0.0, 0.0);
   glShadeModel(GL_FLAT);
}

void display(void)
{
   int i;

   glClear(GL_COLOR_BUFFER_BIT);
/* select white for all lines  */
   glColor3f(1.0, 1.0, 1.0);

/* in 1st row, 3 lines, each with a different stipple  */
   glEnable(GL_LINE_STIPPLE);

   glLineStipple(1, 0x0101);  /*  dotted  */
   drawOneLine(50.0, 125.0, 150.0, 125.0);
   glLineStipple(1, 0x00FF);  /*  dashed  */
   drawOneLine(150.0, 125.0, 250.0, 125.0);
   glLineStipple(1, 0x1C47);  /*  dash/dot/dash  */
   drawOneLine(250.0, 125.0, 350.0, 125.0);

/* in 2nd row, 3 wide lines, each with different stipple */
   glLineWidth(5.0);
   glLineStipple(1, 0x0101);  /*  dotted  */
   drawOneLine(50.0, 100.0, 150.0, 100.0);
   glLineStipple(1, 0x00FF);  /*  dashed  */
   drawOneLine(150.0, 100.0, 250.0, 100.0);
   glLineStipple(1, 0x1C47);  /*  dash/dot/dash  */
   drawOneLine(250.0, 100.0, 350.0, 100.0);
   glLineWidth(1.0);

/* in 3rd row, 6 lines, with dash/dot/dash stipple  */
/* as part of a single connected line strip         */
   glLineStipple(1, 0x1C47);  /*  dash/dot/dash  */
   glBegin(GL_LINE_STRIP);
   for (i = 0; i < 7; i++)
      glVertex2f(50.0 + ((GLfloat) i * 50.0), 75.0);
   glEnd();

/* in 4th row, 6 independent lines with same stipple  */
   for (i = 0; i < 6; i++) {
      drawOneLine(50.0 + ((GLfloat) i * 50.0), 50.0,
                  50.0 + ((GLfloat)(i+1) * 50.0), 50.0);
   }

/* in 5th row, 1 line, with dash/dot/dash stipple    */
/* and a stipple repeat factor of 5                  */
   glLineStipple(5, 0x1C47);  /*  dash/dot/dash  */
   drawOneLine(50.0, 25.0, 350.0, 25.0);

   glDisable(GL_LINE_STIPPLE);
   glFlush();
}

void reshape(int w, int h)
{
   glViewport(0, 0, (GLsizei) w, (GLsizei) h);
   glMatrixMode(GL_PROJECTION);
   glLoadIdentity();
   gluOrtho2D(0.0, (GLdouble) w, 0.0, (GLdouble) h);
}

int main(int argc, char** argv)
{
   glutInit(&argc, argv);
   glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
   glutInitWindowSize(400, 150);
   glutInitWindowPosition(100, 100);
   glutCreateWindow(argv[0]);
   init();
   glutDisplayFunc(display);
   glutReshapeFunc(reshape);
   glutMainLoop();
   return 0;
}

Polygon Details

Polygons are typically drawn by filling in all the pixels enclosed within the boundary, but you can also draw them as outlined polygons or simply as points at the vertices. A filled polygon might be solidly filled or stippled with a certain pattern. Although the exact details are omitted here, filled polygons are drawn in such a way that if adjacent polygons share an edge or vertex, the pixels making up the edge or vertex are drawn exactly once—they’re included in only one of the polygons. This is done so that partially transparent polygons don’t have their edges drawn twice, which would make those edges appear darker (or brighter, depending on what color you’re drawing with). Note that it might result in narrow polygons having no filled pixels in one or more rows or columns of pixels.

To antialias filled polygons, multisampling is highly recommended. For details, see “Antialiasing Geometric Primitives with Multisampling” in Chapter 6.

Polygons as Points, Outlines, or Solids

A polygon has two sides—front and back—and might be rendered differently depending on which side is facing the viewer. This allows you to have cutaway views of solid objects in which there is an obvious distinction between the parts that are inside and those that are outside. By default, both front and back faces are drawn in the same way. To change this, or to draw only outlines or vertices, use glPolygonMode().

For example, you can have the front faces filled and the back faces outlined with two calls to this routine:

glPolygonMode(GL_FRONT, GL_FILL);
glPolygonMode(GL_BACK, GL_LINE);

Reversing and Culling Polygon Faces

By convention, polygons whose vertices appear in counterclockwise order on the screen are called front-facing. You can construct the surface of any “reasonable” solid—a mathematician would call such a surface an orientable manifold (spheres, donuts, and teapots are orientable; Klein bottles and Möbius strips aren’t)—from polygons of consistent orientation. In other words, you can use all clockwise polygons or all counterclockwise polygons. (This is essentially the mathematical definition of orientable.)

Suppose you’ve consistently described a model of an orientable surface but happen to have the clockwise orientation on the outside. You can swap what OpenGL considers the back face by using the function glFrontFace(), supplying the desired orientation for front-facing polygons.

In a completely enclosed surface constructed from opaque polygons with a consistent orientation, none of the back-facing polygons are ever visible—they’re always obscured by the front-facing polygons. If you are outside this surface, you might enable culling to discard polygons that OpenGL determines are back-facing. Similarly, if you are inside the object, only back-facing polygons are visible. To instruct OpenGL to discard front- or back-facing polygons, use the command glCullFace() and enable culling with glEnable().

Advanced

In more technical terms, deciding whether a face of a polygon is front-or back-facing depends on the sign of the polygon’s area computed in window coordinates. One way to compute this area is

02_09_eq201.jpg

where xi and yi are the x and y window coordinates of the ith vertex of the n-vertex polygon and

i⊕1 is (i+1) mod n.

Assuming that GL_CCW has been specified, if a > 0, the polygon corresponding to that vertex is considered to be front-facing; otherwise, it’s back-facing. If GL_CW is specified and if a < 0, then the corresponding polygon is front-facing; otherwise, it’s back-facing.

Try This

try_this.jpg

Modify Example 2-5 by adding some filled polygons. Experiment with different colors. Try different polygon modes. Also, enable culling to see its effect.

Stippling Polygons

By default, filled polygons are drawn with a solid pattern. They can also be filled with a 32-bit by 32-bit window-aligned stipple pattern, which you specify with glPolygonStipple().

Figure 2-10

Figure 2-10 Constructing a Polygon Stipple Pattern

In addition to defining the current polygon stippling pattern, you must enable stippling:

glEnable(GL_POLYGON_STIPPLE);

Use glDisable() with the same argument to disable polygon stippling.

Figure 2-11 shows the results of polygons drawn unstippled and then with two different stippling patterns. The program is shown in Example 2-6. The reversal of white to black (from Figure 2-10 to Figure 2-11) occurs because the program draws in white over a black background, using the pattern in Figure 2-10 as a stencil.

Figure 2-11

Figure 2-11 Stippled Polygons

Example 2-6. Polygon Stipple Patterns: polys.c

void display(void)
{
   GLubyte fly[] = {
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x03, 0x80, 0x01, 0xC0, 0x06, 0xC0, 0x03, 0x60,
      0x04, 0x60, 0x06, 0x20, 0x04, 0x30, 0x0C, 0x20,
      0x04, 0x18, 0x18, 0x20, 0x04, 0x0C, 0x30, 0x20,
      0x04, 0x06, 0x60, 0x20, 0x44, 0x03, 0xC0, 0x22,
      0x44, 0x01, 0x80, 0x22, 0x44, 0x01, 0x80, 0x22,
      0x44, 0x01, 0x80, 0x22, 0x44, 0x01, 0x80, 0x22,
      0x44, 0x01, 0x80, 0x22, 0x44, 0x01, 0x80, 0x22,
      0x66, 0x01, 0x80, 0x66, 0x33, 0x01, 0x80, 0xCC,
      0x19, 0x81, 0x81, 0x98, 0x0C, 0xC1, 0x83, 0x30,
      0x07, 0xe1, 0x87, 0xe0, 0x03, 0x3f, 0xfc, 0xc0,
      0x03, 0x31, 0x8c, 0xc0, 0x03, 0x33, 0xcc, 0xc0,
      0x06, 0x64, 0x26, 0x60, 0x0c, 0xcc, 0x33, 0x30,
      0x18, 0xcc, 0x33, 0x18, 0x10, 0xc4, 0x23, 0x08,
      0x10, 0x63, 0xC6, 0x08, 0x10, 0x30, 0x0c, 0x08,
      0x10, 0x18, 0x18, 0x08, 0x10, 0x00, 0x00, 0x08};

   GLubyte halftone[] = {
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55,
      0xAA, 0xAA, 0xAA, 0xAA, 0x55, 0x55, 0x55, 0x55};

   glClear(GL_COLOR_BUFFER_BIT);
   glColor3f(1.0, 1.0, 1.0);
/*  draw one solid, unstippled rectangle,       */
/*  then two stippled rectangles                */
   glRectf(25.0, 25.0, 125.0, 125.0);
   glEnable(GL_POLYGON_STIPPLE);
   glPolygonStipple(fly);
   glRectf(125.0, 25.0, 225.0, 125.0);
   glPolygonStipple(halftone);
   glRectf(225.0, 25.0, 325.0, 125.0);
   glDisable(GL_POLYGON_STIPPLE);
   glFlush();
}

void init(void)
{
   glClearColor(0.0, 0.0, 0.0, 0.0);
   glShadeModel(GL_FLAT);
}

void reshape(int w, int h)
{
   glViewport(0, 0, (GLsizei) w, (GLsizei) h);
   glMatrixMode(GL_PROJECTION);
   glLoadIdentity();
   gluOrtho2D(0.0, (GLdouble) w, 0.0, (GLdouble) h);
}

int main(int argc, char** argv)
{
   glutInit(&argc, argv);
   glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
   glutInitWindowSize(350, 150);
   glutCreateWindow(argv[0]);
   init();
   glutDisplayFunc(display);
   glutReshapeFunc(reshape);
   glutMainLoop();
   return 0;
}

You might want to use display lists to store polygon stipple patterns to maximize efficiency. (See “Display List Design Philosophy” in Chapter 7.)

Marking Polygon Boundary Edges

Advanced

OpenGL can render only convex polygons, but many nonconvex polygons arise in practice. To draw these nonconvex polygons, you typically subdivide them into convex polygons—usually triangles, as shown in Figure 2-12—and then draw the triangles. Unfortunately, if you decompose a general polygon into triangles and draw the triangles, you can’t really use glPolygonMode() to draw the polygon’s outline, as you get all the triangle outlines inside it. To solve this problem, you can tell OpenGL whether a particular vertex precedes a boundary edge; OpenGL keeps track of this information by passing along with each vertex a bit indicating whether that vertex is followed by a boundary edge. Then, when a polygon is drawn in GL_LINE mode, the nonboundary edges aren’t drawn. In Figure 2-12, the dashed lines represent added edges.

Figure 2-12

Figure 2-12 Subdividing a Nonconvex Polygon

By default, all vertices are marked as preceding a boundary edge, but you can manually control the setting of the edge flag with the command glEdgeFlag*(). This command is used between glBegin() and glEnd() pairs, and it affects all the vertices specified after it until the next glEdgeFlag() call is made. It applies only to vertices specified for polygons, triangles, and quads, not to those specified for strips of triangles or quads.

For instance, Example 2-7 draws the outline shown in Figure 2-13.

Figure 2-13

Figure 2-13 Outlined Polygon Drawn Using Edge Flags

Example 2-7. Marking Polygon Boundary Edges

glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);
glBegin(GL_POLYGON);
    glEdgeFlag(GL_TRUE);
    glVertex3fv(V0);
    glEdgeFlag(GL_FALSE);
    glVertex3fv(V1);
    glEdgeFlag(GL_TRUE);
    glVertex3fv(V2);
glEnd();
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