FreeType » Docs » Support API » Computations

Computations¶

Synopsis¶

This section contains various functions used to perform computations on 16.16 fixed-float numbers or 2d vectors.

Attention: Most arithmetic functions take FT_Long as arguments. For historical reasons, FreeType was designed under the assumption that FT_Long is a 32-bit integer; results can thus be undefined if the arguments don't fit into 32 bits.

FT_MulDiv¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( FT_Long )
  FT_MulDiv( FT_Long  a,
             FT_Long  b,
             FT_Long  c );

Compute ‘(a*b)/c’ with maximum accuracy, using a 64-bit intermediate integer whenever necessary.

This function isn't necessarily as fast as some processor-specific operations, but is at least completely portable.

input

a	The first multiplier.
b	The second multiplier.
c	The divisor.

return

The result of ‘(a*b)/c’. This function never traps when trying to divide by zero; it simply returns ‘MaxInt’ or ‘MinInt’ depending on the signs of ‘a’ and ‘b’.

FT_MulFix¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( FT_Long )
  FT_MulFix( FT_Long  a,
             FT_Long  b );

Compute ‘(a*b)/0x10000’ with maximum accuracy. Its main use is to multiply a given value by a 16.16 fixed-point factor.

input

a	The first multiplier.
b	The second multiplier. Use a 16.16 factor here whenever possible (see note below).

return

The result of ‘(a*b)/0x10000’.

note

This function has been optimized for the case where the absolute value of ‘a’ is less than 2048, and ‘b’ is a 16.16 scaling factor. As this happens mainly when scaling from notional units to fractional pixels in FreeType, it resulted in noticeable speed improvements between versions 2.x and 1.x.

As a conclusion, always try to place a 16.16 factor as the second argument of this function; this can make a great difference.

FT_DivFix¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( FT_Long )
  FT_DivFix( FT_Long  a,
             FT_Long  b );

Compute ‘(a*0x10000)/b’ with maximum accuracy. Its main use is to divide a given value by a 16.16 fixed-point factor.

input

a	The numerator.
b	The denominator. Use a 16.16 factor here.

return

The result of ‘(a*0x10000)/b’.

FT_RoundFix¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( FT_Fixed )
  FT_RoundFix( FT_Fixed  a );

Round a 16.16 fixed number.

input

a	The number to be rounded.

return

‘a’ rounded to the nearest 16.16 fixed integer, halfway cases away from zero.

note

The function uses wrap-around arithmetic.

FT_CeilFix¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( FT_Fixed )
  FT_CeilFix( FT_Fixed  a );

Compute the smallest following integer of a 16.16 fixed number.

input

a	The number for which the ceiling function is to be computed.

return

‘a’ rounded towards plus infinity.

note

The function uses wrap-around arithmetic.

FT_FloorFix¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( FT_Fixed )
  FT_FloorFix( FT_Fixed  a );

Compute the largest previous integer of a 16.16 fixed number.

input

a	The number for which the floor function is to be computed.

return

‘a’ rounded towards minus infinity.

FT_Vector_Transform¶

Defined in FT_FREETYPE_H (freetype/freetype.h).

  FT_EXPORT( void )
  FT_Vector_Transform( FT_Vector*        vec,
                       const FT_Matrix*  matrix );

Transform a single vector through a 2x2 matrix.

inout

vector

The target vector to transform.

input

matrix

A pointer to the source 2x2 matrix.

note

The result is undefined if either ‘vector’ or ‘matrix’ is invalid.

FT_Matrix_Multiply¶

Defined in FT_GLYPH_H (freetype/ftglyph.h).

  FT_EXPORT( void )
  FT_Matrix_Multiply( const FT_Matrix*  a,
                      FT_Matrix*        b );

Perform the matrix operation ‘b = a*b’.

input

a	A pointer to matrix ‘a’.

inout

b	A pointer to matrix ‘b’.

note

The result is undefined if either ‘a’ or ‘b’ is zero.

Since the function uses wrap-around arithmetic, results become meaningless if the arguments are very large.

FT_Matrix_Invert¶

Defined in FT_GLYPH_H (freetype/ftglyph.h).

  FT_EXPORT( FT_Error )
  FT_Matrix_Invert( FT_Matrix*  matrix );

Invert a 2x2 matrix. Return an error if it can't be inverted.

inout

matrix

A pointer to the target matrix. Remains untouched in case of error.

return

FreeType error code. 0 means success.

FT_Angle¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  typedef FT_Fixed  FT_Angle;

This type is used to model angle values in FreeType. Note that the angle is a 16.16 fixed-point value expressed in degrees.

FT_ANGLE_PI¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

#define FT_ANGLE_PI  ( 180L << 16 )

The angle pi expressed in FT_Angle units.

FT_ANGLE_2PI¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

#define FT_ANGLE_2PI  ( FT_ANGLE_PI * 2 )

The angle 2*pi expressed in FT_Angle units.

FT_ANGLE_PI2¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

#define FT_ANGLE_PI2  ( FT_ANGLE_PI / 2 )

The angle pi/2 expressed in FT_Angle units.

FT_ANGLE_PI4¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

#define FT_ANGLE_PI4  ( FT_ANGLE_PI / 4 )

The angle pi/4 expressed in FT_Angle units.

FT_Sin¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( FT_Fixed )
  FT_Sin( FT_Angle  angle );

Return the sinus of a given angle in fixed-point format.

input

angle

The input angle.

return

The sinus value.

note

If you need both the sinus and cosinus for a given angle, use the function FT_Vector_Unit.

FT_Cos¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( FT_Fixed )
  FT_Cos( FT_Angle  angle );

Return the cosinus of a given angle in fixed-point format.

input

angle

The input angle.

return

The cosinus value.

note

If you need both the sinus and cosinus for a given angle, use the function FT_Vector_Unit.

FT_Tan¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( FT_Fixed )
  FT_Tan( FT_Angle  angle );

Return the tangent of a given angle in fixed-point format.

input

angle

The input angle.

return

The tangent value.

FT_Atan2¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( FT_Angle )
  FT_Atan2( FT_Fixed  x,
            FT_Fixed  y );

Return the arc-tangent corresponding to a given vector (x,y) in the 2d plane.

input

x	The horizontal vector coordinate.
y	The vertical vector coordinate.

return

The arc-tangent value (i.e. angle).

FT_Angle_Diff¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( FT_Angle )
  FT_Angle_Diff( FT_Angle  angle1,
                 FT_Angle  angle2 );

Return the difference between two angles. The result is always constrained to the ]-PI..PI] interval.

input

angle1	First angle.
angle2	Second angle.

return

Constrained value of ‘value2-value1’.

FT_Vector_Unit¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( void )
  FT_Vector_Unit( FT_Vector*  vec,
                  FT_Angle    angle );

Return the unit vector corresponding to a given angle. After the call, the value of vec.x will be ‘cos(angle)’, and the value of vec.y will be ‘sin(angle)’.

This function is useful to retrieve both the sinus and cosinus of a given angle quickly.

output

vec	The address of target vector.

input

angle

The input angle.

FT_Vector_Rotate¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( void )
  FT_Vector_Rotate( FT_Vector*  vec,
                    FT_Angle    angle );

Rotate a vector by a given angle.

inout

vec	The address of target vector.

input

angle

The input angle.

FT_Vector_Length¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( FT_Fixed )
  FT_Vector_Length( FT_Vector*  vec );

Return the length of a given vector.

input

vec	The address of target vector.

return

The vector length, expressed in the same units that the original vector coordinates.

FT_Vector_Polarize¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( void )
  FT_Vector_Polarize( FT_Vector*  vec,
                      FT_Fixed   *length,
                      FT_Angle   *angle );

Compute both the length and angle of a given vector.

input

vec	The address of source vector.

output

length	The vector length.
angle	The vector angle.

FT_Vector_From_Polar¶

Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).

  FT_EXPORT( void )
  FT_Vector_From_Polar( FT_Vector*  vec,
                        FT_Fixed    length,
                        FT_Angle    angle );

Compute vector coordinates from a length and angle.

output

vec	The address of source vector.

input

length	The vector length.
angle	The vector angle.