# FreeType-2.9 API Reference

# Computations

## Synopsis

FT_MulDiv |  | FT_Atan2
FT_MulFix | FT_Angle | FT_Angle_Diff
FT_DivFix | FT_ANGLE_PI | FT_Vector_Unit
FT_RoundFix | FT_ANGLE_2PI | FT_Vector_Rotate
FT_CeilFix | FT_ANGLE_PI2 | FT_Vector_Length
FT_FloorFix | FT_ANGLE_PI4 | FT_Vector_Polarize
FT_Vector_Transform | FT_Sin | FT_Vector_From_Polar
FT_Matrix_Multiply | FT_Cos |
FT_Matrix_Invert | FT_Tan |

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

### 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.