Home > Articles > Programming > General Programming/Other Languages

This chapter is from the book


The sequence of letters in Figure 1-13 is built by drawing each character at points around a circle. This figure takes advantage of one of UIKit’s terrific built-in features: NSString instances know how to draw themselves into contexts. You just tell a string to draw at a point or into a rectangle, as in this example:

[@"Hello" drawAtPoint:CGPointMake(100, 50)

The syntax for this call changed in iOS 7, deprecating earlier APIs. Prior to iOS 7, you’d say:

[@"Hello" drawAtPoint:CGPointMake(100, 50) withFont:font]
Figure 1-13

Figure 1-13 Drawing letters in a circle.

This circle progresses clockwise, with a letter deposited every (2 × Pi / 26) radians. Each x and y position was calculated as an offset from a common center. The following code iteratively calculates points around the circle using r × sin(theta) and r × cos(theta), using those points to place each letter:

for (int i = 0; i < 26; i++)
    NSString *letter =
        [alphabet substringWithRange:NSMakeRange(i, 1)];
    CGSize letterSize =
        [letter sizeWithAttributes:@{NSFontAttributeName:font}];

    CGFloat theta = M_PI - i * (2 * M_PI / 26.0);
    CGFloat x = center.x + r * sin(theta) - letterSize.width / 2.0;
    CGFloat y = center.y + r * cos(theta) - letterSize.height / 2.0;

    [letter drawAtPoint:CGPointMake(x, y)

This is an acceptable way to approach this challenge, but you could greatly improve it by leveraging context transforms.

Transform State

Every context stores a 2D affine transform as part of its state. This transform is called the current transform matrix. It specifies how to rotate, translate, and scale the context while drawing. It provides a powerful and flexible way to create advanced drawing operations. Contrast the layout shown in Figure 1-14 with the one in Figure 1-13. This improvement is achieved through the magic of context transforms.

Figure 1-14

Figure 1-14 Drawing letters in a circle using transforms.

Listing 1-12 shows the steps that went into creating this. It consists of a series of transform operations that rotate the canvas and draw each letter. Context save and restore operations ensure that the only transform that persists from one drawing operation to the next is the one that appears in boldface in the listing. This translation sets the context’s origin to its center point.

This enables the context to freely rotate around that point, so each letter can be drawn at an exact radius. Moving to the left by half of each letter width ensures that every letter is drawn centered around the point at the end of that radius.

Listing 1-12 Transforming Contexts During Drawing


// Start drawing
CGContextRef context = UIGraphicsGetCurrentContext();

// Retrieve the center and set a radius
CGPoint center = RectGetCenter(bounds);
CGFloat r = center.x * 0.75f;

// Start by adjusting the context origin
// This affects all subsequent operations
CGContextTranslateCTM(context, center.x, center.y);

// Iterate through the alphabet
for (int i = 0; i < 26; i++)
    // Retrieve the letter and measure its display size
    NSString *letter =
        [alphabet substringWithRange:NSMakeRange(i, 1)];
    CGSize letterSize =
        [letter sizeWithAttributes:@{NSFontAttributeName:font}];

    // Calculate the current angular offset
    CGFloat theta = i * (2 * M_PI / (float) 26);

    // Encapsulate each stage of the drawing

    // Rotate the context
    CGContextRotateCTM(context, theta);

    // Translate up to the edge of the radius and move left by
    // half the letter width. The height translation is negative
    // as this drawing sequence uses the UIKit coordinate system.
    // Transformations that move up go to lower y values.
    CGContextTranslateCTM(context, -letterSize.width / 2, -r);

    // Draw the letter and pop the transform state
    [letter drawAtPoint:CGPointMake(0, 0)

// Retrieve and return the image
UIImage *image = UIGraphicsGetImageFromCurrentImageContext();
return image;

Building a More Exacting Layout

A more pedantic solution to drawing the letters in a circle avoids the extra spacing around the I and the squeezing around the W. Listing 1-13 details the steps needed to create the more precise layout shown in Figure 1-15. This example demonstrates finer layout placement.

Figure 1-15

Figure 1-15 This version uses better spacing, based on the width of each letter.

Start by calculating the total width of the layout. Sum the width of each individual letter (as done here) or just measure the string as a whole. This enables you to mark your progress along the layout, producing a percentage of travel from beginning to end.

Next, adjust the placement for each letter based on the percentage consumed by each iteration. Use this percentage to calculate a rotation angle for laying down the letter.

Finish by drawing the letter just as you did in Listing 1-12. What you end up with is a layout that respects the width of each letter, moving forward proportionately according to the letter’s natural size.

Listing 1-13 Precise Text Placement Around a Circle

// Calculate the full extent
CGFloat fullSize = 0;
for (int i = 0; i < 26; i++)
    NSString *letter =
        [alphabet substringWithRange:NSMakeRange(i, 1)];
    CGSize letterSize =
        [letter sizeWithAttributes:@{NSFontAttributeName:font}];
    fullSize += letterSize.width;

// Initialize the consumed space
CGFloat consumedSize = 0.0f;

// Iterate through each letter, consuming that width
for (int i = 0; i < 26; i++)
    // Measure each letter
    NSString *letter =
        [alphabet substringWithRange:NSMakeRange(i, 1)];
    CGSize letterSize =
        [letter sizeWithAttributes:@{NSFontAttributeName:font}];

    // Move the pointer forward, calculating the
    // new percentage of travel along the path
    consumedSize += letterSize.width / 2.0f;
    CGFloat percent = consumedSize / fullSize;
    CGFloat theta = percent * 2 * M_PI;
    consumedSize += letterSize.width / 2.0f;

    // Prepare to draw the letter by saving the state

    // Rotate the context by the calculated angle
    CGContextRotateCTM(context, theta);

    // Move to the letter position
    CGContextTranslateCTM(context, -letterSize.width / 2, -r);

    // Draw the letter
    [letter drawAtPoint:CGPointMake(0, 0) withFont:font];

    // Reset the context back to the way it was

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.


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.


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.


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.


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


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


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.


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.


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