Legacy Document
Important: The information in this document is obsolete and should not be used for new development.
Important: The information in this document is obsolete and should not be used for new development.
Chapter 8 - QuickDraw GX Mathematics
This chapter describes QuickDraw GX number formats, number-format conversions, mathematical functions, and functions that operate on mappings (transformation matrices). Read this chapter if your application requires the explicit use of any of the mathematical capabilities of QuickDraw GX.Related information on how QuickDraw GX uses mappings can be found in the chapter "Transform Objects" and the chapter "View-Related Objects" in Inside Macintosh: QuickDraw GX Objects.
This chapter first describes the number formats used in QuickDraw GX. It then describes the number-format conversion macros and mathematical functions that are provided by QuickDraw GX. It then shows how to use QuickDraw GX macros and functions to provide
- fixed-point number conversions
- fixed-point operations
- operations on 64-bit numbers
- vector operations
- Cartesian and polar coordinate conversions
- random number generation
- roots of linear and quadratic equations
- bit analysis
- mapping operations
Chapter Contents
- About QuickDraw GX Mathematics
- Number Formats
- Integer Formats
- Floating-Point Formats
- Fixed-Point Formats
- Working With Bias in Fixed-Point Operations
- Number-Conversion Macros
- Mathematical Functions
- Operations on Fixed, long, and fract Numbers
- Operations on wide Numbers
- Vector Operations
- Cartesian and Polar Coordinate Conversion
- Random Number Generation
- Roots of Linear and Quadratic Equations
- Bit Analysis
- Transformation Operations With Mappings
- Characteristics of a Mapping
- Translation by a Relative Amount
- Translation to a Specified Point
- Scaling
- Rotation
- Skewing
- Perspective
- Using QuickDraw GX Mathematics
- Converting Number Formats
- Performing Fixed-Point Operations
- Converting Between Cartesian and Polar Coordinates
- Performing Vector Operations
- Shifting the Bits of a wide Number
- Determining the Highest Order Bit of a wide Number
- Generating Random Numbers
- Analyzing the Bits in a Number
- Resetting a Mapping
- QuickDraw GX Mathematics Reference
- Constants and Data Types
- Number Formats and Constants
- The Mapping Structure
- Number-Conversion Macros
- Format Conversions
- Rounding, Truncating, and Square Root Operations
- Mathematical Functions
- Fixed-Point Operations
- Operations on wide Numbers
- Vector Operations
- Cartesian and Polar Coordinate Point Conversions
- Random Number Generation
- Linear and Quadratic Roots
- Bit Analysis
- Mapping Functions
- Manipulating and Applying Mappings
- Modifying Mappings
- Summary of QuickDraw GX Mathematics
- Constants and Data Types
- Number Formats and Constants
- The Mapping Structure
- Number-Conversion Macros
- Format Conversions
- Rounding, Truncating, and Square Root Operations
- Mathematical Functions
- Fixed-Point Operations
- Operations on wide Numbers
- Vector Operations
- Cartesian and Polar Coordinate Point Conversions
- Random Number Generation
- Linear and Quadratic Roots
- Bit Analysis
- Mapping Functions
- Manipulating and Applying Mappings
- Modifying Mappings