Home > Articles > Programming > Graphic Programming

This chapter is from the book

This chapter is from the book

Building Solid Objects

Composing a solid object out of triangles (or any other polygon) involves more than assembling a series of vertices in a 3D coordinate space. Let's examine the sample program TRIANGLE, which uses two triangle fans to create a cone in our viewing volume. The first fan produces the cone shape, using the first vertex as the point of the cone and the remaining vertices as points along a circle further down the z-axis. The second fan forms a circle and lies entirely in the xy plane, making up the bottom surface of the cone.

The output from TRIANGLE is shown in Figure 3.18. Here, you are looking directly down the z-axis and can see only a circle composed of a fan of triangles. The individual triangles are emphasized by coloring them alternately green and red.

The code for the SetupRC and RenderScene functions is shown in Listing 3.8. (This listing contains some unfamiliar variables and specifiers that are explained shortly.) This program demonstrates several aspects of composing 3D objects. Right-click in the window, and you will notice an Effects menu; it will be used to enable and disable some 3D drawing features so we can explore some of the characteristics of 3D object creation. We describe these features as we progress.

Figure 3.18Figure 3.18 Initial output from the TRIANGLE sample program.

Listing 3.8 SetupRC and RenderScene Code for the TRIANGLE Sample Program

// This function does any needed initialization on the rendering
// context.
void SetupRC()
  {
  // Black background
  glClearColor(0.0f, 0.0f, 0.0f, 1.0f );


  // Set drawing color to green
  glColor3f(0.0f, 1.0f, 0.0f);


  // Set color shading model to flat
  glShadeModel(GL_FLAT);


  // Clockwise-wound polygons are front facing; this is reversed
  // because we are using triangle fans
  glFrontFace(GL_CW);
  }




// Called to draw scene
void RenderScene(void)
  {
  GLfloat x,y,angle;     // Storage for coordinates and angles
  int iPivot = 1;        // Used to flag alternating colors


  // Clear the window and the depth buffer
  glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);


  // Turn culling on if flag is set
  if(bCull)
    glEnable(GL_CULL_FACE);
  else
    glDisable(GL_CULL_FACE);


  // Enable depth testing if flag is set
  if(bDepth)
    glEnable(GL_DEPTH_TEST);
  else
    glDisable(GL_DEPTH_TEST);


  // Draw the back side as a wireframe only, if flag is set
  if(bOutline)
    glPolygonMode(GL_BACK,GL_LINE);
  else
    glPolygonMode(GL_BACK,GL_FILL);


  // Save matrix state and do the rotation
  glPushMatrix();
  glRotatef(xRot, 1.0f, 0.0f, 0.0f);
  glRotatef(yRot, 0.0f, 1.0f, 0.0f);



  // Begin a triangle fan
  glBegin(GL_TRIANGLE_FAN);


  // Pinnacle of cone is shared vertex for fan, moved up z-axis
  // to produce a cone instead of a circle
  glVertex3f(0.0f, 0.0f, 75.0f);


  // Loop around in a circle and specify even points along the circle
  // as the vertices of the triangle fan
  for(angle = 0.0f; angle < (2.0f*GL_PI); angle += (GL_PI/8.0f))
    {
    // Calculate x and y position of the next vertex
    x = 50.0f*sin(angle);
    y = 50.0f*cos(angle);

    // Alternate color between red and green
    if((iPivot %2) == 0)
      glColor3f(0.0f, 1.0f, 0.0f);
    else
      glColor3f(1.0f, 0.0f, 0.0f);

    // Increment pivot to change color next time
    iPivot++;

    // Specify the next vertex for the triangle fan
    glVertex2f(x, y);
    }

  // Done drawing fan for cone
  glEnd();


  // Begin a new triangle fan to cover the bottom
  glBegin(GL_TRIANGLE_FAN);

  // Center of fan is at the origin
  glVertex2f(0.0f, 0.0f);
  for(angle = 0.0f; angle < (2.0f*GL_PI); angle += (GL_PI/8.0f))
    {
    // Calculate x and y position of the next vertex
    x = 50.0f*sin(angle);
    y = 50.0f*cos(angle);

    // Alternate color between red and green
    if((iPivot %2) == 0)
      glColor3f(0.0f, 1.0f, 0.0f);
    else
      glColor3f(1.0f, 0.0f, 0.0f);

    // Increment pivot to change color next time
    iPivot++;

    // Specify the next vertex for the triangle fan
    glVertex2f(x, y);
    }

  // Done drawing the fan that covers the bottom
  glEnd();

  // Restore transformations
  glPopMatrix();

  // Flush drawing commands
  glFlush();
  }

Setting Polygon Colors

Until now, we have set the current color only once and drawn only a single shape. Now, with multiple polygons, things get slightly more interesting. We want to use different colors so we can see our work more easily. Colors are actually specified per vertex, not per polygon. The shading model affects whether the polygon is solidly colored (using the current color selected when the last vertex was specified) or smoothly shaded between the colors specified for each vertex.

The line

glShadeModel(GL_FLAT);

tells OpenGL to fill the polygons with the solid color that was current when the polygon's last vertex was specified. This is why we can simply change the current color to red or green before specifying the next vertex in our triangle fan. On the other hand, the line

glShadeModel(GL_SMOOTH);

would tell OpenGL to shade the triangles smoothly from each vertex, attempting to interpolate the colors between those specified for each vertex. You'll learn much more about color and shading in Chapter 5.

Hidden Surface Removal

Hold down one of the arrow keys to spin the cone around, and don't select anything from the Effects menu yet. You'll notice something unsettling: The cone appears to be swinging back and forth plus and minus 180°, with the bottom of the cone always facing you, but not rotating a full 360°. Figure 3.19 shows this effect more clearly.

Figure 3.19Figure 3.19 The rotating cone appears to be wobbling back and forth.

This wobbling happens because the bottom of the cone is drawn after the sides of the cone are drawn. No matter how the cone is oriented, the bottom is drawn on top of it, producing the "wobbling" illusion. This effect is not limited to the various sides and parts of an object. If more than one object is drawn and one is in front of the other (from the viewer's perspective), the last object drawn still appears over the previously drawn object.

You can correct this peculiarity with a simple feature called depth testing. Depth testing is an effective technique for hidden surface removal, and OpenGL has functions that do this for you behind the scenes. The concept is simple: When a pixel is drawn, it is assigned a value (called the z value) that denotes its distance from the viewer's perspective. Later, when another pixel needs to be drawn to that screen location, the new pixel's z value is compared to that of the pixel that is already stored there. If the new pixel's z value is higher, it is closer to the viewer and thus in front of the previous pixel, so the previous pixel is obscured by the new pixel. If the new pixel's z value is lower, it must be behind the existing pixel and thus is not obscured. This maneuver is accomplished internally by a depth buffer with storage for a depth value for every pixel on the screen. Most all of the samples in this book use depth testing.

To enable depth testing, simply call

glEnable(GL_DEPTH_TEST);

Depth testing is enabled in Listing 3.8 when the bDepth variable is set to True, and it is disabled if bDepth is False:

// Enable depth testing if flag is set
if(bDepth)
  glEnable(GL_DEPTH_TEST);
else
  glDisable(GL_DEPTH_TEST);

The bDepth variable is set when you select Depth Test from the Effects menu. In addition, the depth buffer must be cleared each time the scene is rendered. The depth buffer is analogous to the color buffer in that it contains information about the distance of the pixels from the observer. This information is used to determine whether any pixels are hidden by pixels closer to the observer:

// Clear the window and the depth buffer
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

A right-click with the mouse opens a pop-up menu that allows you to toggle depth testing on and off. Figure 3.20 shows the TRIANGLE program with depth testing enabled. It also shows the cone with the bottom correctly hidden behind the sides. You can see that depth testing is practically a prerequisite for creating 3D objects out of solid polygons.

Figure 3.20Figure 3.20 The bottom of the cone is now correctly placed behind the sides for this orientation.

Culling: Hiding Surfaces for Performance

You can see that there are obvious visual advantages to not drawing a surface that is obstructed by another. Even so, you pay some performance overhead because every pixel drawn must be compared with the previous pixel's z value. Sometimes, however, you know that a surface will never be drawn anyway, so why specify it? Culling is the term used to describe the technique of eliminating geometry that we know will never be seen. By not sending this geometry to your OpenGL driver and hardware, you can make significant performance improvements. One culling technique is backface culling, which eliminates the backsides of a surface.

In our working example, the cone is a closed surface, and we never see the inside. OpenGL is actually (internally) drawing the back sides of the far side of the cone and then the front sides of the polygons facing us. Then, by a comparison of z buffer values, the far side of the cone is either overwritten or ignored. Figures 3.21a and 3.21b show our cone at a particular orientation with depth testing turned on (a) and off (b). Notice that the green and red triangles that make up the cone sides change when depth testing is enabled. Without depth testing, the sides of the triangles at the far side of the cone show through.

Figure 3.21aFigure 3.21a With depth testing.

Figure 3.21bFigure 3.21b Without depth testing.

Earlier in the chapter, we explained how OpenGL uses winding to determine the front and back sides of polygons and that it is important to keep the polygons that define the outside of our objects wound in a consistent direction. This consistency is what allows us to tell OpenGL to render only the front, only the back, or both sides of polygons. By eliminating the back sides of the polygons, we can drastically reduce the amount of necessary processing to render the image. Even though depth testing will eliminate the appearance of the inside of objects, internally OpenGL must take them into account unless we explicitly tell it not to.

Backface culling is enabled or disabled for our program by the following code from Listing 3.8:

  // Clockwise-wound polygons are front facing; this is reversed
  // because we are using triangle fans
  glFrontFace(GL_CW);
...
...


  // Turn culling on if flag is set
  if(bCull)
    glEnable(GL_CULL_FACE);
  else
    glDisable(GL_CULL_FACE);

Note that we first changed the definition of front-facing polygons to assume clockwise winding (because our triangle fans are all wound clockwise).

Figure 3.22 demonstrates that the bottom of the cone is gone when culling is enabled. The reason is that we didn't follow our own rule about all the surface polygons having the same winding. The triangle fan that makes up the bottom of the cone is wound clockwise, like the fan that makes up the sides of the cone, but the front side of the cone's bottom section is then facing the inside (see Figure 3.23).

Figure 3.22Figure 3.22 The bottom of the cone is culled because the front-facing triangles are inside.

Figure 3.23Figure 3.23 How the cone was assembled from two triangle fans.

We could have corrected this problem by changing the winding rule, by calling

glFrontFace(GL_CCW);

just before we drew the second triangle fan. But in this example, we wanted to make it easy for you to see culling in action, as well as set up for our next demonstration of polygon tweaking.

Why Do We Need Backface Culling?

You might wonder, "If backface culling is so desirable, why do we need the ability to turn it on and off?" Backface culling is useful when drawing closed objects or solids, but you won't always be rendering these types of geometry. Some flat objects (such as paper) can still be seen from both sides. If the cone we are drawing here were made of glass or plastic, you would actually be able to see the front and the back sides of the geometry. (See Chapter 6 for a discussion of drawing transparent objects.)

Polygon Modes

Polygons don't have to be filled with the current color. By default, polygons are drawn solid, but you can change this behavior by specifying that polygons are to be drawn as outlines or just points (only the vertices are plotted). The function glPolygonMode allows polygons to be rendered as filled solids, as outlines, or as points only. In addition, you can apply this rendering mode to both sides of the polygons or only to the front or back. The following code from Listing 3.8 shows the polygon mode being set to outlines or solid, depending on the state of the Boolean variable bOutline:

// Draw back side as a polygon only, if flag is set
if(bOutline)
  glPolygonMode(GL_BACK,GL_LINE);
else
  glPolygonMode(GL_BACK,GL_FILL);

Figure 3.24 shows the back sides of all polygons rendered as outlines. (We had to disable culling to produce this image; otherwise, the inside would be eliminated and you would get no outlines.) Notice that the bottom of the cone is now wireframe instead of solid, and you can see up inside the cone where the inside walls are also drawn as wireframe triangles.

Figure 3.24Figure 3.24 Using glPolygonMode to render one side of the triangles as outlines.

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020