ES-DE/external/lunasvg/3rdparty/plutovg/plutovg-ft-math.h

437 lines
14 KiB
C

/***************************************************************************/
/* */
/* fttrigon.h */
/* */
/* FreeType trigonometric functions (specification). */
/* */
/* Copyright 2001, 2003, 2005, 2007, 2013 by */
/* David Turner, Robert Wilhelm, and Werner Lemberg. */
/* */
/* This file is part of the FreeType project, and may only be used, */
/* modified, and distributed under the terms of the FreeType project */
/* license, LICENSE.TXT. By continuing to use, modify, or distribute */
/* this file you indicate that you have read the license and */
/* understand and accept it fully. */
/* */
/***************************************************************************/
#ifndef PLUTOVG_FT_MATH_H
#define PLUTOVG_FT_MATH_H
#include "plutovg-ft-types.h"
/*************************************************************************/
/* */
/* The min and max functions missing in C. As usual, be careful not to */
/* write things like PVG_FT_MIN( a++, b++ ) to avoid side effects. */
/* */
#define PVG_FT_MIN( a, b ) ( (a) < (b) ? (a) : (b) )
#define PVG_FT_MAX( a, b ) ( (a) > (b) ? (a) : (b) )
#define PVG_FT_ABS( a ) ( (a) < 0 ? -(a) : (a) )
/*
* Approximate sqrt(x*x+y*y) using the `alpha max plus beta min'
* algorithm. We use alpha = 1, beta = 3/8, giving us results with a
* largest error less than 7% compared to the exact value.
*/
#define PVG_FT_HYPOT( x, y ) \
( x = PVG_FT_ABS( x ), \
y = PVG_FT_ABS( y ), \
x > y ? x + ( 3 * y >> 3 ) \
: y + ( 3 * x >> 3 ) )
/*************************************************************************/
/* */
/* <Function> */
/* PVG_FT_MulFix */
/* */
/* <Description> */
/* A very simple function used to perform the computation */
/* `(a*b)/0x10000' with maximum accuracy. Most of the time this is */
/* used 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. */
/* */
PVG_FT_Long
PVG_FT_MulFix( PVG_FT_Long a,
PVG_FT_Long b );
/*************************************************************************/
/* */
/* <Function> */
/* PVG_FT_MulDiv */
/* */
/* <Description> */
/* A very simple function used to perform the computation `(a*b)/c' */
/* with maximum accuracy (it uses 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'. */
/* */
PVG_FT_Long
PVG_FT_MulDiv( PVG_FT_Long a,
PVG_FT_Long b,
PVG_FT_Long c );
/*************************************************************************/
/* */
/* <Function> */
/* PVG_FT_DivFix */
/* */
/* <Description> */
/* A very simple function used to perform the computation */
/* `(a*0x10000)/b' with maximum accuracy. Most of the time, this is */
/* used 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'. */
/* */
PVG_FT_Long
PVG_FT_DivFix( PVG_FT_Long a,
PVG_FT_Long b );
/*************************************************************************/
/* */
/* <Section> */
/* computations */
/* */
/*************************************************************************/
/*************************************************************************
*
* @type:
* PVG_FT_Angle
*
* @description:
* This type is used to model angle values in FreeType. Note that the
* angle is a 16.16 fixed-point value expressed in degrees.
*
*/
typedef PVG_FT_Fixed PVG_FT_Angle;
/*************************************************************************
*
* @macro:
* PVG_FT_ANGLE_PI
*
* @description:
* The angle pi expressed in @PVG_FT_Angle units.
*
*/
#define PVG_FT_ANGLE_PI ( 180L << 16 )
/*************************************************************************
*
* @macro:
* PVG_FT_ANGLE_2PI
*
* @description:
* The angle 2*pi expressed in @PVG_FT_Angle units.
*
*/
#define PVG_FT_ANGLE_2PI ( PVG_FT_ANGLE_PI * 2 )
/*************************************************************************
*
* @macro:
* PVG_FT_ANGLE_PI2
*
* @description:
* The angle pi/2 expressed in @PVG_FT_Angle units.
*
*/
#define PVG_FT_ANGLE_PI2 ( PVG_FT_ANGLE_PI / 2 )
/*************************************************************************
*
* @macro:
* PVG_FT_ANGLE_PI4
*
* @description:
* The angle pi/4 expressed in @PVG_FT_Angle units.
*
*/
#define PVG_FT_ANGLE_PI4 ( PVG_FT_ANGLE_PI / 4 )
/*************************************************************************
*
* @function:
* PVG_FT_Sin
*
* @description:
* 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 @PVG_FT_Vector_Unit.
*
*/
PVG_FT_Fixed
PVG_FT_Sin( PVG_FT_Angle angle );
/*************************************************************************
*
* @function:
* PVG_FT_Cos
*
* @description:
* 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 @PVG_FT_Vector_Unit.
*
*/
PVG_FT_Fixed
PVG_FT_Cos( PVG_FT_Angle angle );
/*************************************************************************
*
* @function:
* PVG_FT_Tan
*
* @description:
* Return the tangent of a given angle in fixed-point format.
*
* @input:
* angle ::
* The input angle.
*
* @return:
* The tangent value.
*
*/
PVG_FT_Fixed
PVG_FT_Tan( PVG_FT_Angle angle );
/*************************************************************************
*
* @function:
* PVG_FT_Atan2
*
* @description:
* 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).
*
*/
PVG_FT_Angle
PVG_FT_Atan2( PVG_FT_Fixed x,
PVG_FT_Fixed y );
/*************************************************************************
*
* @function:
* PVG_FT_Angle_Diff
*
* @description:
* 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'.
*
*/
PVG_FT_Angle
PVG_FT_Angle_Diff( PVG_FT_Angle angle1,
PVG_FT_Angle angle2 );
/*************************************************************************
*
* @function:
* PVG_FT_Vector_Unit
*
* @description:
* Return the unit vector corresponding to a given angle. After the
* call, the value of `vec.x' will be `sin(angle)', and the value of
* `vec.y' will be `cos(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.
*
*/
void
PVG_FT_Vector_Unit( PVG_FT_Vector* vec,
PVG_FT_Angle angle );
/*************************************************************************
*
* @function:
* PVG_FT_Vector_Rotate
*
* @description:
* Rotate a vector by a given angle.
*
* @inout:
* vec ::
* The address of target vector.
*
* @input:
* angle ::
* The input angle.
*
*/
void
PVG_FT_Vector_Rotate( PVG_FT_Vector* vec,
PVG_FT_Angle angle );
/*************************************************************************
*
* @function:
* PVG_FT_Vector_Length
*
* @description:
* 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.
*
*/
PVG_FT_Fixed
PVG_FT_Vector_Length( PVG_FT_Vector* vec );
/*************************************************************************
*
* @function:
* PVG_FT_Vector_Polarize
*
* @description:
* 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.
*
*/
void
PVG_FT_Vector_Polarize( PVG_FT_Vector* vec,
PVG_FT_Fixed *length,
PVG_FT_Angle *angle );
/*************************************************************************
*
* @function:
* PVG_FT_Vector_From_Polar
*
* @description:
* Compute vector coordinates from a length and angle.
*
* @output:
* vec ::
* The address of source vector.
*
* @input:
* length ::
* The vector length.
*
* angle ::
* The vector angle.
*
*/
void
PVG_FT_Vector_From_Polar( PVG_FT_Vector* vec,
PVG_FT_Fixed length,
PVG_FT_Angle angle );
#endif /* PLUTOVG_FT_MATH_H */