3dcam-headers/math.c

#include "math.h"

// Stolen from grumpycoder
// this is from here : https://github.com/grumpycoders/Balau/blob/master/tests/test-Handles.cc#L20-L102

// precalc costable

static int m_cosTable[512];                     

static const unsigned int DC_2PI = 2048;        

static const unsigned int DC_PI  = 1024;

static const unsigned int DC_PI2 = 512;

// f(n) = cos(n * 2pi / 2048) <- 2048 is == DC_2PI value
// f(n) = 2 * f(1) * f(n - 1) - f(n - 2)

void generateTable(void){
    
    m_cosTable[0] = 16777216;               // 2^24 * cos(0 * 2pi / 2048) => 2^24 * 1 = 2^24 : here, 2^24 defines the precision we want after the decimal point

    static const long long C = 16777137;    // 2^24 * cos(1 * 2pi / 2048) = C = f(1);

    m_cosTable[1] = C;
    
    for (int i = 2; i < 512; i++){

        m_cosTable[i] = ((C * m_cosTable[i - 1]) >> 23) - m_cosTable[i - 2];

        m_cosTable[511] = 0;
    }
};

int ncos(unsigned int t) {

    t %= DC_2PI;

    int r;

    if (t < DC_PI2) {

        r = m_cosTable[t];

    } else if (t < DC_PI) {

        r = -m_cosTable[DC_PI - 1 - t];

    } else if (t < (DC_PI + DC_PI2)) {

        r = -m_cosTable[t - DC_PI];

    } else {

        r = m_cosTable[DC_2PI - 1 - t];

    };

    return r >> 12;
};

// sin(x) = cos(x - pi / 2)

int nsin(unsigned int t) {

    t %= DC_2PI;

    if (t < DC_PI2){

        return ncos(t + DC_2PI - DC_PI2);

    };

    return ncos(t - DC_PI2);
};

// https://github.com/Arsunt/TR2Main/blob/411cacb35914c616cb7960c0e677e00c71c7ee88/3dsystem/phd_math.cpp#L432
long long patan(long x, long y){

    long long result;

    int swapBuf;

    int flags = 0;
    
    // if either x or y are 0, return 0

    if( x == 0 && y == 0){

        return 0;

    }

    if( x < 0 ) {

        flags |= 4; 

        x = -x;
        
    }
    
    if ( y < 0 ) {

        flags |= 2;

        y = -y;

    }
    
    if ( y > x ) {

        flags |= 1;

        SWAP(x, y ,swapBuf);

    }
    
    result = AtanBaseTable[flags] + AtanAngleTable[0x800 * y / x];

    if ( result < 0 ){

        result = -result;
        
    return result;
    
    }
    
};

u_int psqrt(u_int n){
    
    u_int result = 0;
    
    u_int base = 0x40000000;
    
    u_int basedResult;
    
    for( ; base != 0; base >>= 2 ) {
    
        for( ; base != 0; base >>= 2 ) {
    
            basedResult = base + result;
    
            result >>= 1;
            
            if( basedResult > n ) {
       
                break;
       
            }
            
            n -= basedResult;
       
            result |= base;
       
        }
    
    }
    
    return result;
};

// From : https://github.com/grumpycoders/pcsx-redux/blob/7438e9995833db5bc1e14da735bbf9dc78300f0b/src/mips/shell/math.h

int32_t dMul(int32_t a, int32_t b) {
 
    long long r = a;
 
    r *= b;
 
    return r >> 24;

};

// standard lerp function
//  s = source, an arbitrary number up to 2^24
//  d = destination, an arbitrary number up to 2^24
//  p = position, a number between 0 and 256, inclusive
//  p = 0 means output = s
//  p = 256 means output = d

uint32_t lerpU(uint32_t start, uint32_t dest, unsigned pos) {
    
    return (start * (256 - pos) + dest * pos) >> 8; 

};

int32_t lerpS(int32_t start, int32_t dest, unsigned pos) {
    
    return (start * (256 - pos) + dest * pos) >> 8;

};

// start, dest and pos have to be << x, then the result has to be >> x where x defines precision: 
// precision = 2^24 - 2^x
// << x : 0 < pos < precision
// https://discord.com/channels/642647820683444236/646765703143227394/811318550978494505
// my angles are between 0 and 2048 (full circle), so 2^11 for the range of angles; with numbers on a 8.24 representation, a 1.0 angle (or 2pi) means it's 2^24, so to "convert" my angles from 8.24 to my internal discrete cos, I only have to shift by 13

int32_t lerpD(int32_t start, int32_t dest, int32_t pos) {
    
     return dMul(start, 16777216 - pos) + dMul(dest, pos);

};

long long lerpL(long long start, long long dest, long long pos) {
    
    return dMul( (start << 12), 16777216 - (pos << 12) ) + dMul((dest << 12), (pos << 12) ) >> 12;

};

int lerp(int start, int end, int factor){
    
    // lerp interpolated cam movement
    // InBetween = Value 1 + ( ( Value2 - Value1 ) * lerpValue ) ;
    // lerpValue should be a int between 17 and 256.
    
    
    return ( ( start ) + ( ( end - start ) * factor ) ) >> 12;

};

long long easeIn(long long i){
 
    return ((i << 7) * (i << 7) * (i << 7) / 32 ) >> 19;
 
};

int easeOut(int i){

    return (4096 >> 7) - ((4096 - (i << 7)) * (4096 - (i << 7))) >> 12;

};
    
//~ int easeInOut(int i, int div){
    
    //~ return lerp(easeIn(i, div), easeOut(i) , i);
    
//~ };
    
SVECTOR SVlerp(SVECTOR start, SVECTOR end, int factor){

    SVECTOR output = {0,0,0,0};

    output.vx = lerp(start.vx, end.vx, factor);

    output.vy = lerp(start.vy, end.vy, factor);

    output.vz = lerp(start.vz, end.vz, factor);

    return output;

};

VECTOR getVectorTo( VECTOR actor, VECTOR target ) {
    
    // Returns a normalized vector that points from actor to target
    
    VECTOR direction = { subVector(target, actor) };
    
    VECTOR Ndirection = {0,0,0,0};
    
    u_int distSq = (direction.vx * direction.vx) + (direction.vz * direction.vz);
    
    direction.pad = psqrt(distSq);
    
    VectorNormal(&direction, &Ndirection);
    
    return Ndirection ;

};