Maths.c File Reference

Mathematic utilities. More...

#include <math.h>
#include "Gpu_Hal.h"
#include "Maths.h"

Go to the source code of this file.

Macros
#define	doubleswap(x, y)   {double z = x;x=y;y=z;}
	Use PROGMEM.
#define	xyzswap(x, y)   {Math_3d_Xyz_t z = x;x=y;y=z;}

Functions
int16_t	Math_Qsin (uint16_t a)
	Sin function.
int16_t	Math_Qcos (uint16_t a)
	Cos function.
void	Math_Polarxy (int32_t r, float th, int32_t *x, int32_t *y, int32_t ox, int32_t oy)
	Polar function.
float	Math_Da (float i, int16_t degree)
	Da function 1 uint = 0.5 degree. 1 circle = 720 degree.
float	Math_Power (float x, unsigned int y)
uint32_t	Math_Points_Distance (uint32_t x1, uint32_t y1, uint32_t x2, uint32_t y2)
uint32_t	Math_Points_Nearby_NextX (uint32_t x1, uint32_t y1, uint32_t y2, uint32_t Distance)
void	Normalise (Math_3d_Xyz_t *p)
Math_3d_Xyz_t	Math_3D_ArbitraryRotate (Math_3d_Xyz_t p, double theta, Math_3d_Xyz_t r)
Math_3d_Xyz_t	Math_3D_ArbitraryRotate2 (Math_3d_Xyz_t p, double theta, Math_3d_Xyz_t p1, Math_3d_Xyz_t p2)
static Math_3d_Xyz_t	subVector (Math_3d_Xyz_t p1, Math_3d_Xyz_t p2)
static Math_3d_Xyz_t	normalVector (Math_3d_Xyz_t p1, Math_3d_Xyz_t p2)
static double	dotProduct (Math_3d_Xyz_t a, Math_3d_Xyz_t b)
int	Math_3D_Backface_Find_Visible (Math_3d_Face_t face, Math_3d_Xyz_t view)

Variables
PROGMEM prog_uint16_t	sintab []

Detailed Description

Mathematic utilities.

Author

Tuan Nguyen tuan..nosp@m.nguy.nosp@m.en@br.nosp@m.tchi.nosp@m.p.com

Date

2019

MIT License

Copyright (c) [2019] [Bridgetek Pte Ltd (BRTChip)]

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Definition in file Maths.c.

Macro Definition Documentation

doubleswap

#define doubleswap	(		x,
			y
	)		{double z = x;x=y;y=z;}

Use PROGMEM.

Definition at line 37 of file Maths.c.

xyzswap

#define xyzswap	(		x,
			y
	)		{Math_3d_Xyz_t z = x;x=y;y=z;}

Definition at line 38 of file Maths.c.

Function Documentation

dotProduct()

static double dotProduct ( Math_3d_Xyz_t  a, Math_3d_Xyz_t  b  )

static

Definition at line 247 of file Maths.c.

                                                           {
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

Math_3D_ArbitraryRotate()

Math_3d_Xyz_t Math_3D_ArbitraryRotate	(	Math_3d_Xyz_t	p,
		double	theta,
		Math_3d_Xyz_t	r
	)

Definition at line 161 of file Maths.c.

                                                                                      {
    Math_3d_Xyz_t q = { 0.0,0.0,0.0 };
    double costheta;
    double sintheta;
 
    Normalise(&r);
    costheta = cos(theta);
    sintheta = sin(theta);
 
    q.x += (costheta + (1 - costheta) * r.x * r.x) * p.x;
    q.x += ((1 - costheta) * r.x * r.y - r.z * sintheta) * p.y;
    q.x += ((1 - costheta) * r.x * r.z + r.y * sintheta) * p.z;
 
    q.y += ((1 - costheta) * r.x * r.y + r.z * sintheta) * p.x;
    q.y += (costheta + (1 - costheta) * r.y * r.y) * p.y;
    q.y += ((1 - costheta) * r.y * r.z - r.x * sintheta) * p.z;
 
    q.z += ((1 - costheta) * r.x * r.z - r.y * sintheta) * p.x;
    q.z += ((1 - costheta) * r.y * r.z + r.x * sintheta) * p.y;
    q.z += (costheta + (1 - costheta) * r.z * r.z) * p.z;
 
    return(q);
}

Math_3D_ArbitraryRotate2()

Math_3d_Xyz_t Math_3D_ArbitraryRotate2	(	Math_3d_Xyz_t	p,
		double	theta,
		Math_3d_Xyz_t	p1,
		Math_3d_Xyz_t	p2
	)

Definition at line 192 of file Maths.c.

{
    Math_3d_Xyz_t q = { 0.0,0.0,0.0 };
    double costheta;
    double sintheta;
    Math_3d_Xyz_t r;
 
    r.x = p2.x - p1.x;
    r.y = p2.y - p1.y;
    r.z = p2.z - p1.z;
    p.x -= p1.x;
    p.y -= p1.y;
    p.z -= p1.z;
    Normalise(&r);
 
    sintheta = sin(theta);
    costheta = cos(theta);
 
    q.y += ((1 - costheta) * r.x * r.y + r.z * sintheta) * p.x;
    q.y += (costheta + (1 - costheta) * r.y * r.y) * p.y;
    q.y += ((1 - costheta) * r.y * r.z - r.x * sintheta) * p.z;
 
    q.x += (costheta + (1 - costheta) * r.x * r.x) * p.x;
    q.x += ((1 - costheta) * r.x * r.y - r.z * sintheta) * p.y;
    q.x += ((1 - costheta) * r.x * r.z + r.y * sintheta) * p.z;
 
    q.z += ((1 - costheta) * r.x * r.z - r.y * sintheta) * p.x;
    q.z += ((1 - costheta) * r.y * r.z + r.x * sintheta) * p.y;
    q.z += (costheta + (1 - costheta) * r.z * r.z) * p.z;
 
    q.x += p1.x;
    q.y += p1.y;
    q.z += p1.z;
    return(q);
}

Math_3D_Backface_Find_Visible()

int Math_3D_Backface_Find_Visible	(	Math_3d_Face_t	face,
		Math_3d_Xyz_t	view
	)

Definition at line 251 of file Maths.c.

                                                                           {
    Math_3d_Xyz_t v12 = subVector(face.p2, face.p1);
    Math_3d_Xyz_t v13 = subVector(face.p3, face.p1);
    Math_3d_Xyz_t N = normalVector(v12, v13);
    Math_3d_Xyz_t S = subVector(view, face.p1);
 
    double Dot = dotProduct(N, S);
 
    return Dot >= 0;
}

Math_Da()

float Math_Da	(	float	i,
		int16_t	degree
	)

Da function 1 uint = 0.5 degree. 1 circle = 720 degree.

Parameters

i
degree

Returns

float

Definition at line 111 of file Maths.c.

{
    return (i - degree) * 32768 / 360;
}

Math_Points_Distance()

uint32_t Math_Points_Distance	(	uint32_t	x1,
		uint32_t	y1,
		uint32_t	x2,
		uint32_t	y2
	)

Definition at line 126 of file Maths.c.

                                                                                  {
    return (uint32_t)sqrt((double)(Math_Power((float)(x2 - x1), 2) + Math_Power((float)(y2 - y1), 2)));
}

Math_Points_Nearby_NextX()

uint32_t Math_Points_Nearby_NextX	(	uint32_t	x1,
		uint32_t	y1,
		uint32_t	y2,
		uint32_t	Distance
	)

Definition at line 130 of file Maths.c.

                                                                                            {
    return (uint32_t)sqrt((double)Math_Power((float)Distance, 2) - Math_Power((float)abs(y2 - y1), 2)) + x1;
}

Math_Polarxy()

void Math_Polarxy	(	int32_t	r,
		float	th,
		int32_t *	x,
		int32_t *	y,
		int32_t	ox,
		int32_t	oy
	)

Polar function.

Parameters

r
th
x
y
ox
oy

Definition at line 97 of file Maths.c.

                                                                                       {
    *x = (16 * ox) + (((long)r * Math_Qsin((uint16_t)th)) >> 11) + 16;
    *y = (16 * oy) - (((long)r * Math_Qcos((uint16_t)th)) >> 11);
}

Math_Power()

float Math_Power	(	float	x,
		unsigned int	y
	)

Definition at line 116 of file Maths.c.

{
    if (y == 0)
        return 1;
    else if (y % 2 == 0)
        return Math_Power(x, y / 2) * Math_Power(x, y / 2);
    else
        return x * Math_Power(x, y / 2) * Math_Power(x, y / 2);
}

Math_Qcos()

int16_t Math_Qcos

(

uint16_t

a

)

Cos function.

Parameters

a

Angle

Returns

int16_t

Definition at line 82 of file Maths.c.

{
    return (Math_Qsin(a + 16384));
}

Math_Qsin()

int16_t Math_Qsin

(

uint16_t

a

)

Sin function.

Parameters

a

Angle

Returns

int16_t

Definition at line 58 of file Maths.c.

{
    uint8_t f;
    int16_t s0;
    int16_t s1;
 
    if (a & 32768) {
        return -Math_Qsin(a & 32767);
    }
    if (a & 16384) {
        a = 32768 - a;
    }
    f = a & 127;
    s0 = pgm_read_word(sintab + (a >> 7));
    s1 = pgm_read_word(sintab + (a >> 7) + 1);
    return (int16_t)(s0 + (int16_t)((int32_t)f * (s1 - s0) >> 7));
}

Normalise()

void Normalise

(

Math_3d_Xyz_t *

p

)

Definition at line 137 of file Maths.c.

{
    double length;
 
    length = sqrt(p->x * p->x + p->y * p->y + p->z * p->z);
    if (length != 0) {
        p->x /= length;
        p->y /= length;
        p->z /= length;
    }
    else {
        p->x = 0;
        p->y = 0;
        p->z = 0;
    }
}

normalVector()

static Math_3d_Xyz_t normalVector ( Math_3d_Xyz_t  p1, Math_3d_Xyz_t  p2  )

static

Definition at line 237 of file Maths.c.

                                                                      {
    Math_3d_Xyz_t n;
 
    n.x = p1.y * p2.z - p1.z * p2.y;
    n.y = p1.z * p2.x - p1.x * p2.z;
    n.z = p1.x * p2.y - p1.y * p2.x;
 
    return n;
}

subVector()

static Math_3d_Xyz_t subVector ( Math_3d_Xyz_t  p1, Math_3d_Xyz_t  p2  )

static

Definition at line 228 of file Maths.c.

                                                                   {
    Math_3d_Xyz_t ret;
    ret.x = p1.x - p2.x;
    ret.y = p1.y - p2.y;
    ret.z = p1.z - p2.z;
 
    return ret;
}

Variable Documentation

sintab

PROGMEM prog_uint16_t sintab[]

Initial value:

= {
    0, 402, 804, 1206, 1607, 2009, 2410, 2811, 3211, 3611, 4011, 4409, 4807, 5205, 5601, 5997, 6392,
    6786, 7179, 7571, 7961, 8351, 8739, 9126, 9511, 9895, 10278, 10659, 11038, 11416, 11792, 12166, 12539,
    12909, 13278, 13645, 14009, 14372, 14732, 15090, 15446, 15799, 16150, 16499, 16845, 17189, 17530, 17868,
    18204, 18537, 18867, 19194, 19519, 19840, 20159, 20474, 20787, 21096, 21402, 21705, 22004, 22301, 22594,
    22883, 23169, 23452, 23731, 24006, 24278, 24546, 24811, 25072, 25329, 25582, 25831, 26077, 26318, 26556, 26789,
    27019, 27244, 27466, 27683, 27896, 28105, 28309, 28510, 28706, 28897, 29085, 29268, 29446, 29621, 29790, 29955,
    30116, 30272, 30424, 30571, 30713, 30851, 30984, 31113, 31236, 31356, 31470, 31580, 31684, 31785, 31880, 31970,
    32056, 32137, 32213, 32284, 32350, 32412, 32468, 32520, 32567, 32609, 32646, 32678, 32705, 32727, 32744, 32757,
    32764, 32767, 32764 }

Definition at line 41 of file Maths.c.

                                 {
    0, 402, 804, 1206, 1607, 2009, 2410, 2811, 3211, 3611, 4011, 4409, 4807, 5205, 5601, 5997, 6392,
    6786, 7179, 7571, 7961, 8351, 8739, 9126, 9511, 9895, 10278, 10659, 11038, 11416, 11792, 12166, 12539,
    12909, 13278, 13645, 14009, 14372, 14732, 15090, 15446, 15799, 16150, 16499, 16845, 17189, 17530, 17868,
    18204, 18537, 18867, 19194, 19519, 19840, 20159, 20474, 20787, 21096, 21402, 21705, 22004, 22301, 22594,
    22883, 23169, 23452, 23731, 24006, 24278, 24546, 24811, 25072, 25329, 25582, 25831, 26077, 26318, 26556, 26789,
    27019, 27244, 27466, 27683, 27896, 28105, 28309, 28510, 28706, 28897, 29085, 29268, 29446, 29621, 29790, 29955,
    30116, 30272, 30424, 30571, 30713, 30851, 30984, 31113, 31236, 31356, 31470, 31580, 31684, 31785, 31880, 31970,
    32056, 32137, 32213, 32284, 32350, 32412, 32468, 32520, 32567, 32609, 32646, 32678, 32705, 32727, 32744, 32757,
    32764, 32767, 32764 };