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This section contains various functions used to perform computations on 16.16 fixed-float numbers or 2d vectors.
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.
The first multiplier.
The second multiplier.
The divisor.
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_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.
The second multiplier. Use a 16.16 factor here whenever possible (see note below).
The result of ‘(a*b)/0x10000’.
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_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.
The numerator.
The denominator. Use a 16.16 factor here.
The result of ‘(a*0x10000)/b’.
FT_EXPORT( FT_Fixed ) FT_RoundFix( FT_Fixed a );
Round a 16.16 fixed number.
The number to be rounded.
‘a’ rounded to the nearest 16.16 fixed integer, halfway cases away from zero.
The function uses wrap-around arithmetic.
FT_EXPORT( FT_Fixed ) FT_CeilFix( FT_Fixed a );
Compute the smallest following integer of a 16.16 fixed number.
The number for which the ceiling function is to be computed.
‘a’ rounded towards plus infinity.
FT_EXPORT( FT_Fixed ) FT_FloorFix( FT_Fixed a );
Compute the largest previous integer of a 16.16 fixed number.
The number for which the floor function is to be computed.
‘a’ rounded towards minus infinity.
FT_EXPORT( void ) FT_Vector_Transform( FT_Vector* vec, const FT_Matrix* matrix );
Transform a single vector through a 2x2 matrix.
The target vector to transform.
A pointer to the source 2x2 matrix.
The result is undefined if either ‘vector’ or ‘matrix’ is invalid.
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’.
A pointer to matrix ‘a’.
A pointer to matrix ‘b’.
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_EXPORT( FT_Error ) FT_Matrix_Invert( FT_Matrix* matrix );
Invert a 2x2 matrix. Return an error if it can't be inverted.
A pointer to the target matrix. Remains untouched in case of error.
FreeType error code. 0 means success.
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.
#define FT_ANGLE_PI ( 180L << 16 )
The angle pi expressed in FT_Angle units.
#define FT_ANGLE_2PI ( FT_ANGLE_PI * 2 )
The angle 2*pi expressed in FT_Angle units.
#define FT_ANGLE_PI2 ( FT_ANGLE_PI / 2 )
The angle pi/2 expressed in FT_Angle units.
#define FT_ANGLE_PI4 ( FT_ANGLE_PI / 4 )
The angle pi/4 expressed in FT_Angle units.
FT_EXPORT( FT_Fixed ) FT_Sin( FT_Angle angle );
Return the sinus of a given angle in fixed-point format.
The input angle.
The sinus value.
If you need both the sinus and cosinus for a given angle, use the function FT_Vector_Unit.
FT_EXPORT( FT_Fixed ) FT_Cos( FT_Angle angle );
Return the cosinus of a given angle in fixed-point format.
The cosinus value.
FT_EXPORT( FT_Fixed ) FT_Tan( FT_Angle angle );
Return the tangent of a given angle in fixed-point format.
The tangent value.
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.
The horizontal vector coordinate.
The vertical vector coordinate.
The arc-tangent value (i.e. angle).
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.
First angle.
Second angle.
Constrained value of ‘value2-value1’.
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.
The address of target vector.
FT_EXPORT( void ) FT_Vector_Rotate( FT_Vector* vec, FT_Angle angle );
Rotate a vector by a given angle.
FT_EXPORT( FT_Fixed ) FT_Vector_Length( FT_Vector* vec );
Return the length of a given vector.
The vector length, expressed in the same units that the original vector coordinates.
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.
The address of source vector.
The vector length.
The vector angle.
FT_EXPORT( void ) FT_Vector_From_Polar( FT_Vector* vec, FT_Fixed length, FT_Angle angle );
Compute vector coordinates from a length and angle.