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439 lines
14 KiB
C
439 lines
14 KiB
C
#ifndef SW_FT_MATH_H
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#define SW_FT_MATH_H
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/***************************************************************************/
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/* */
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/* fttrigon.h */
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/* */
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/* FreeType trigonometric functions (specification). */
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/* */
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/* Copyright 2001, 2003, 2005, 2007, 2013 by */
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/* David Turner, Robert Wilhelm, and Werner Lemberg. */
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/* */
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/* This file is part of the FreeType project, and may only be used, */
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/* modified, and distributed under the terms of the FreeType project */
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/* license, LICENSE.TXT. By continuing to use, modify, or distribute */
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/* this file you indicate that you have read the license and */
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/* understand and accept it fully. */
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/* */
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/***************************************************************************/
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#include "sw_ft_types.h"
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/*************************************************************************/
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/* */
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/* The min and max functions missing in C. As usual, be careful not to */
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/* write things like SW_FT_MIN( a++, b++ ) to avoid side effects. */
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/* */
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#define SW_FT_MIN( a, b ) ( (a) < (b) ? (a) : (b) )
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#define SW_FT_MAX( a, b ) ( (a) > (b) ? (a) : (b) )
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#define SW_FT_ABS( a ) ( (a) < 0 ? -(a) : (a) )
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/*
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* Approximate sqrt(x*x+y*y) using the `alpha max plus beta min'
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* algorithm. We use alpha = 1, beta = 3/8, giving us results with a
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* largest error less than 7% compared to the exact value.
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*/
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#define SW_FT_HYPOT( x, y ) \
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( x = SW_FT_ABS( x ), \
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y = SW_FT_ABS( y ), \
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x > y ? x + ( 3 * y >> 3 ) \
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: y + ( 3 * x >> 3 ) )
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/*************************************************************************/
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/* */
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/* <Function> */
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/* SW_FT_MulFix */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation */
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/* `(a*b)/0x10000' with maximum accuracy. Most of the time this is */
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/* used to multiply a given value by a 16.16 fixed-point factor. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. Use a 16.16 factor here whenever */
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/* possible (see note below). */
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/* */
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/* <Return> */
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/* The result of `(a*b)/0x10000'. */
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/* */
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/* <Note> */
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/* This function has been optimized for the case where the absolute */
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/* value of `a' is less than 2048, and `b' is a 16.16 scaling factor. */
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/* As this happens mainly when scaling from notional units to */
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/* fractional pixels in FreeType, it resulted in noticeable speed */
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/* improvements between versions 2.x and 1.x. */
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/* */
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/* As a conclusion, always try to place a 16.16 factor as the */
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/* _second_ argument of this function; this can make a great */
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/* difference. */
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/* */
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SW_FT_Long
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SW_FT_MulFix( SW_FT_Long a,
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SW_FT_Long b );
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/*************************************************************************/
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/* */
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/* <Function> */
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/* SW_FT_MulDiv */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation `(a*b)/c' */
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/* with maximum accuracy (it uses a 64-bit intermediate integer */
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/* whenever necessary). */
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/* */
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/* This function isn't necessarily as fast as some processor specific */
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/* operations, but is at least completely portable. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. */
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/* c :: The divisor. */
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/* */
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/* <Return> */
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/* The result of `(a*b)/c'. This function never traps when trying to */
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/* divide by zero; it simply returns `MaxInt' or `MinInt' depending */
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/* on the signs of `a' and `b'. */
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/* */
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SW_FT_Long
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SW_FT_MulDiv( SW_FT_Long a,
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SW_FT_Long b,
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SW_FT_Long c );
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/*************************************************************************/
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/* */
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/* <Function> */
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/* SW_FT_DivFix */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation */
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/* `(a*0x10000)/b' with maximum accuracy. Most of the time, this is */
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/* used to divide a given value by a 16.16 fixed-point factor. */
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/* */
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/* <Input> */
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/* a :: The numerator. */
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/* b :: The denominator. Use a 16.16 factor here. */
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/* */
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/* <Return> */
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/* The result of `(a*0x10000)/b'. */
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/* */
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SW_FT_Long
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SW_FT_DivFix( SW_FT_Long a,
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SW_FT_Long b );
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/*************************************************************************/
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/* */
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/* <Section> */
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/* computations */
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/* */
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/*************************************************************************/
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/*************************************************************************
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*
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* @type:
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* SW_FT_Angle
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*
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* @description:
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* This type is used to model angle values in FreeType. Note that the
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* angle is a 16.16 fixed-point value expressed in degrees.
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*
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*/
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typedef SW_FT_Fixed SW_FT_Angle;
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/*************************************************************************
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*
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* @macro:
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* SW_FT_ANGLE_PI
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*
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* @description:
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* The angle pi expressed in @SW_FT_Angle units.
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*
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*/
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#define SW_FT_ANGLE_PI ( 180L << 16 )
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/*************************************************************************
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*
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* @macro:
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* SW_FT_ANGLE_2PI
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*
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* @description:
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* The angle 2*pi expressed in @SW_FT_Angle units.
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*
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*/
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#define SW_FT_ANGLE_2PI ( SW_FT_ANGLE_PI * 2 )
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/*************************************************************************
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*
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* @macro:
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* SW_FT_ANGLE_PI2
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*
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* @description:
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* The angle pi/2 expressed in @SW_FT_Angle units.
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*
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*/
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#define SW_FT_ANGLE_PI2 ( SW_FT_ANGLE_PI / 2 )
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/*************************************************************************
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*
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* @macro:
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* SW_FT_ANGLE_PI4
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*
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* @description:
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* The angle pi/4 expressed in @SW_FT_Angle units.
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*
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*/
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#define SW_FT_ANGLE_PI4 ( SW_FT_ANGLE_PI / 4 )
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/*************************************************************************
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*
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* @function:
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* SW_FT_Sin
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*
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* @description:
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* Return the sinus of a given angle in fixed-point format.
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*
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* @input:
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* angle ::
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* The input angle.
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*
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* @return:
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* The sinus value.
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*
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* @note:
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* If you need both the sinus and cosinus for a given angle, use the
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* function @SW_FT_Vector_Unit.
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*
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*/
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SW_FT_Fixed
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SW_FT_Sin( SW_FT_Angle angle );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Cos
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*
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* @description:
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* Return the cosinus of a given angle in fixed-point format.
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*
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* @input:
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* angle ::
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* The input angle.
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*
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* @return:
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* The cosinus value.
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*
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* @note:
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* If you need both the sinus and cosinus for a given angle, use the
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* function @SW_FT_Vector_Unit.
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*
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*/
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SW_FT_Fixed
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SW_FT_Cos( SW_FT_Angle angle );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Tan
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*
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* @description:
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* Return the tangent of a given angle in fixed-point format.
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*
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* @input:
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* angle ::
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* The input angle.
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*
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* @return:
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* The tangent value.
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*
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*/
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SW_FT_Fixed
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SW_FT_Tan( SW_FT_Angle angle );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Atan2
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*
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* @description:
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* Return the arc-tangent corresponding to a given vector (x,y) in
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* the 2d plane.
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*
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* @input:
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* x ::
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* The horizontal vector coordinate.
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*
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* y ::
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* The vertical vector coordinate.
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*
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* @return:
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* The arc-tangent value (i.e. angle).
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*
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*/
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SW_FT_Angle
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SW_FT_Atan2( SW_FT_Fixed x,
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SW_FT_Fixed y );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Angle_Diff
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*
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* @description:
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* Return the difference between two angles. The result is always
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* constrained to the ]-PI..PI] interval.
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*
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* @input:
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* angle1 ::
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* First angle.
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*
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* angle2 ::
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* Second angle.
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*
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* @return:
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* Constrained value of `value2-value1'.
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*
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*/
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SW_FT_Angle
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SW_FT_Angle_Diff( SW_FT_Angle angle1,
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SW_FT_Angle angle2 );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Vector_Unit
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*
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* @description:
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* Return the unit vector corresponding to a given angle. After the
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* call, the value of `vec.x' will be `sin(angle)', and the value of
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* `vec.y' will be `cos(angle)'.
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*
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* This function is useful to retrieve both the sinus and cosinus of a
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* given angle quickly.
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*
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* @output:
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* vec ::
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* The address of target vector.
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*
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* @input:
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* angle ::
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* The input angle.
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*
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*/
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void
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SW_FT_Vector_Unit( SW_FT_Vector* vec,
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SW_FT_Angle angle );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Vector_Rotate
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*
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* @description:
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* Rotate a vector by a given angle.
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*
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* @inout:
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* vec ::
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* The address of target vector.
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*
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* @input:
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* angle ::
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* The input angle.
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*
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*/
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void
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SW_FT_Vector_Rotate( SW_FT_Vector* vec,
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SW_FT_Angle angle );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Vector_Length
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*
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* @description:
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* Return the length of a given vector.
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*
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* @input:
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* vec ::
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* The address of target vector.
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*
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* @return:
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* The vector length, expressed in the same units that the original
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* vector coordinates.
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*
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*/
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SW_FT_Fixed
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SW_FT_Vector_Length( SW_FT_Vector* vec );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Vector_Polarize
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*
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* @description:
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* Compute both the length and angle of a given vector.
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*
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* @input:
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* vec ::
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* The address of source vector.
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*
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* @output:
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* length ::
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* The vector length.
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*
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* angle ::
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* The vector angle.
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*
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*/
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void
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SW_FT_Vector_Polarize( SW_FT_Vector* vec,
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SW_FT_Fixed *length,
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SW_FT_Angle *angle );
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/*************************************************************************
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*
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* @function:
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* SW_FT_Vector_From_Polar
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*
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* @description:
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* Compute vector coordinates from a length and angle.
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*
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* @output:
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* vec ::
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* The address of source vector.
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*
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* @input:
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* length ::
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* The vector length.
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*
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* angle ::
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* The vector angle.
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*
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*/
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void
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SW_FT_Vector_From_Polar( SW_FT_Vector* vec,
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SW_FT_Fixed length,
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SW_FT_Angle angle );
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#endif // SW_FT_MATH_H
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