Documentation
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Overview ¶
Package math2d provides a set of fixed-point 2D operations that work with image.Point vectors and int32 angles.
The angle unit is equal to 1/4294967296 of the full angle. The int32 type can represent angles from -FullAngle/2 to FullAngle/2 - 1 (inclusive).
The fixed-point CORDIC algorithm used by this package is at least 10 times faster than using math.Cos and math.Sin on the ISA that does not support cos/sin in hardware. If the ISA provides hardware cos/sin the CORDIC is about 2 times slower than using math.Cos/math.Sin but it does not use FPU context which could be an advantage in some cases.
The accuracy of the fixed-point CORDIC algorithm depends on many factors but is usually much worse than the accuracy of any algorithm based on cos/sin and floating-point calculations (see "Numerical Accuracy and Hardware Tradeoffs for CORDIC Arithmetic for Special Purpose Processors", K. Kota, J. Cavallaro, http://scholarship.rice.edu/bitstream/handle/1911/20039/Kot1993Jul1NumericalA.PDF)
Index ¶
Constants ¶
const ( FullAngle = 1 << 32 // 2π rad = 360° RightAngle int32 = FullAngle / 4 // π/2 rad = 90° )
Angle constants. FullAngle does not fit in int32 but can be used to calculate smaller angle constants.
Variables ¶
This section is empty.
Functions ¶
func A ¶
A converts an integer vector to a fixed-point one ensuring that both f.X and f.Y values fit in the n-bit signed fixed-point number and at last one of f.X or f.Y has exactly n-1 significant bits plus a sign bit. A returns the converted vector and the length of its fractional part (can be negative if the number of significant bits was reduced). For zero v it returns (v, n-1). Use A to normalize the vector before passing it to the Rotate or Polar functions to improve accuracy.
func F ¶
F returns image.Point{v.X<<n, v.Y<<n}. It provides a convenient way to convert an integer vector to a fixed-point one. If you want to ensure a specific number of significant bits use A instead.
func I ¶
I provides a convenient way to convert a fixed-point vector to an integer one. It supports positive and negative n so it can be used to invert F and A as below
I(F(v, n), n) == v // true if no overflow I(A(v, n)) == v // true if no overflow and no significant bit reduction
func Polar ¶
Polar returns the polar form of v. The internal calculations require that v.Mul(2) must not overflow.
func Rotate ¶
Rotate rotates the vector v by the given angle.
Rotate can also be used to convert a vector in the polar form (R, theta) to the rectangular one as below
Rotate(image.Pt(R, 0), theta)
Moreover, it can be used to calculate trigonometric functions as below
Rotate(image.Pt(1<<n, 0), alpha)
The returned vector contains {cos(alpha), sin(alpha)} with n-bit fractional part. Since the cosine and sine are calculated simultaneously, the returned vector can be also thought of as a fractional representation of tangent and cotangent.
The internal calculations require that v.Mul(2) must not overflow.
Types ¶
This section is empty.
Source Files