Rasterizer.h

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//
// Copyright 2020 Arvind Singh
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; If not, see <http://www.gnu.org/licenses/>.
#ifndef _TGX_RASTERIZER_H_
#define _TGX_RASTERIZER_H_
 
 
// only C++, no plain C
#ifdef __cplusplus
 
 
#include "ShaderParams.h"
 
namespace tgx
{
 
#define TGX_RASTERIZE_SUBPIXEL_BITS (6)
 
#define TGX_RASTERIZE_SUBPIXEL256 (1 << TGX_RASTERIZE_SUBPIXEL_BITS)
#define TGX_RASTERIZE_SUBPIXEL128 (1 << (TGX_RASTERIZE_SUBPIXEL_BITS -1))
#define TGX_RASTERIZE_MULT256(X) ((X) << (TGX_RASTERIZE_SUBPIXEL_BITS))
#define TGX_RASTERIZE_MULT128(X) ((X) << (TGX_RASTERIZE_SUBPIXEL_BITS -1))
#define TGX_RASTERIZE_DIV256(X) ((X) >> (TGX_RASTERIZE_SUBPIXEL_BITS))
 
 
 
 
TGX_INLINE inline void minmax3_i32(const int32_t a, const int32_t b, const int32_t c, int32_t& mn, int32_t& mx)
    {
    if (a < b) { mn = a; mx = b; } else { mn = b; mx = a; }
    if (c < mn) { mn = c; } else if (c > mx) { mx = c; }
    }
 
 
TGX_INLINE inline int32_t tgx_floor_div_subpixel_i32(const int32_t x)
    {
#if defined(__GNUC__) || defined(__clang__)
    // Assumes arithmetic right shift for signed integers: his is what GCC/Clang generate on ARM, Xtensa, etc.
    return x >> TGX_RASTERIZE_SUBPIXEL_BITS;
#else
    // Portable mathematical floor(x / S), S > 0.
    const int32_t S = TGX_RASTERIZE_SUBPIXEL256;
    return (x >= 0) ? (x / S) : -(((-x) + S - 1) / S);
#endif
    }
 
 
TGX_INLINE inline int32_t tgx_ceil_div_subpixel_i32(const int32_t x)
    {
#if defined(__GNUC__) || defined(__clang__)
    // ceil(x / S) == floor((x + S - 1) / S) for positive power-of-two S, assuming no overflow in x + S - 1.
    return (x + (TGX_RASTERIZE_SUBPIXEL256 - 1)) >> TGX_RASTERIZE_SUBPIXEL_BITS;
#else
    // Portable mathematical ceil(x / S), S > 0.
    const int32_t S = TGX_RASTERIZE_SUBPIXEL256;
    return (x >= 0) ? ((x + S - 1) / S) : -((-x) / S);
#endif
    }
 
 
 
 
    template<auto shader_function, typename RASTERIZER_PARAMS>
    TGX_INLINE inline void rasterizeTriangle(const int LX, const int LY, const RasterizerVec4 & V0, const RasterizerVec4 & V1, const RasterizerVec4 & V2, const int32_t offset_x, const int32_t offset_y, const RASTERIZER_PARAMS & data)
        {
        // assuming that clipping was already perfomed and that V0, V1, V2 are in a reasonable "range" so no overflow will occur.
        const int32_t hx = TGX_RASTERIZE_MULT128(LX);
        const int32_t hy = TGX_RASTERIZE_MULT128(LY);
        const float mx = (float)(hx);
        const float my = (float)(hy);
 
        const iVec2  P0(lfloorf(V0.x * mx), lfloorf(V0.y * my));
        const iVec2 sP1(lfloorf(V1.x * mx), lfloorf(V1.y * my));
        const iVec2 sP2(lfloorf(V2.x * mx), lfloorf(V2.y * my));
 
        int32_t umx, uMx, umy, uMy;
        minmax3_i32(P0.x, sP1.x, sP2.x, umx, uMx);
        minmax3_i32(P0.y, sP1.y, sP2.y, umy, uMy);
 
        const int32_t bx0 = umx + hx - TGX_RASTERIZE_SUBPIXEL128;
        const int32_t bx1 = uMx + hx - TGX_RASTERIZE_SUBPIXEL128;
        const int32_t by0 = umy + hy - TGX_RASTERIZE_SUBPIXEL128;
        const int32_t by1 = uMy + hy - TGX_RASTERIZE_SUBPIXEL128;
        int32_t xmin = tgx_ceil_div_subpixel_i32(bx0);
        int32_t xmax = tgx_floor_div_subpixel_i32(bx1);
        int32_t ymin = tgx_ceil_div_subpixel_i32(by0);
        int32_t ymax = tgx_floor_div_subpixel_i32(by1);
 
        //if ((xmin > xmax) || (ymin > ymax)) return;
 
        // Intersect the sub-image with the triangle bounding box.
        int32_t sx = data.im->lx();
        int32_t sy = data.im->ly();
        int32_t ox = offset_x;
        int32_t oy = offset_y;
 
        if (ox < xmin) { sx -= (xmin - ox); ox = xmin; }
        if (ox + sx > xmax) { sx = xmax - ox + 1; }
        if (sx <= 0) return;
 
        if (oy < ymin) { sy -= (ymin - oy); oy = ymin; }
        if (oy + sy > ymax) { sy = ymax - oy + 1; }
        if (sy <= 0) return;
 
        const uint32_t bw = (uint32_t)uMx - (uint32_t)umx;
        const uint32_t bh = (uint32_t)uMy - (uint32_t)umy;
        const bool c32 = ((bw < 32768u) && (bh < 32768u));
        int32_t a;
        if (c32)
            { // 32 bits computation
            a = (((sP2.x - P0.x) * (sP1.y - P0.y)) - ((sP2.y - P0.y) * (sP1.x - P0.x)));
            if (a == 0) return;
            }
        else
            { // 64 bits computations
            const int64_t a64 = (((int64_t)(sP2.x - P0.x)) * ((int64_t)(sP1.y - P0.y))) - (((int64_t)(sP2.y - P0.y)) * ((int64_t)(sP1.x - P0.x)));
            if (a64 == 0) return;
            a = (a64 > 0) ? 1 : -1;
            }
 
        const RasterizerVec4& fP1 = (a > 0) ? V1 : V2;
        const RasterizerVec4& fP2 = (a > 0) ? V2 : V1;
        const iVec2& P1 = (a > 0) ? sP1 : sP2;
        const iVec2& P2 = (a > 0) ? sP2 : sP1;
 
        const int32_t us = TGX_RASTERIZE_MULT256(ox) - hx + TGX_RASTERIZE_SUBPIXEL128;   // start pixel position
        const int32_t vs = TGX_RASTERIZE_MULT256(oy) - hy + TGX_RASTERIZE_SUBPIXEL128;   //
 
        ox -= offset_x;
        oy -= offset_y;
 
        int32_t dx1 = P1.y - P0.y;
        int32_t dy1 = P0.x - P1.x;
        int32_t dx2 = P2.y - P1.y;
        int32_t dy2 = P1.x - P2.x;
        int32_t dx3 = P0.y - P2.y;
        int32_t dy3 = P2.x - P0.x;
 
        int32_t O1, O2, O3;
 
        if (c32)
            { // 32 bits computation            
            O1 = ((us - P0.x) * dx1) + ((vs - P0.y) * dy1);
            O3 = ((us - P2.x) * dx3) + ((vs - P2.y) * dy3);
 
            // Before top-left correction: O1 + O2 + O3 = A32. Use unsigned arithmetic to avoid signed-overflow UB in the reconstruction.
            const int32_t A32 = (a > 0) ? a : -a;
            O2 = (int32_t)((uint32_t)A32 - (uint32_t)O1 - (uint32_t)O3);
 
            if ((dx1 < 0) || ((dx1 == 0) && (dy1 < 0))) O1--;
            if ((dx2 < 0) || ((dx2 == 0) && (dy2 < 0))) O2--;
            if ((dx3 < 0) || ((dx3 == 0) && (dy3 < 0))) O3--;
 
            dx1 *= TGX_RASTERIZE_SUBPIXEL256;
            dy1 *= TGX_RASTERIZE_SUBPIXEL256;
            dx2 *= TGX_RASTERIZE_SUBPIXEL256;
            dy2 *= TGX_RASTERIZE_SUBPIXEL256;
            dx3 *= TGX_RASTERIZE_SUBPIXEL256;
            dy3 *= TGX_RASTERIZE_SUBPIXEL256;
            }
        else
            { // 64 bits computation
            int64_t dO1 = (((int64_t)(us - P0.x)) * ((int64_t)dx1)) + (((int64_t)(vs - P0.y)) * ((int64_t)dy1));
            if ((dx1 < 0) || ((dx1 == 0) && (dy1 < 0))) dO1--; // top left rule (beware, changes total aera).
            O1 = (dO1 >= 0) ? ((int32_t)TGX_RASTERIZE_DIV256(dO1)) : -((int32_t)TGX_RASTERIZE_DIV256(-dO1 + (TGX_RASTERIZE_SUBPIXEL256 - 1)));
 
            int64_t dO2 = (((int64_t)(us - P1.x)) * ((int64_t)dx2)) + (((int64_t)(vs - P1.y)) * ((int64_t)dy2));
            if ((dx2 < 0) || ((dx2 == 0) && (dy2 < 0))) dO2--; // top left rule (beware, changes total aera).
            O2 = (dO2 >= 0) ? ((int32_t)TGX_RASTERIZE_DIV256(dO2)) : -((int32_t)TGX_RASTERIZE_DIV256(-dO2 + (TGX_RASTERIZE_SUBPIXEL256 - 1)));
 
            int64_t dO3 = (((int64_t)(us - P2.x)) * ((int64_t)dx3)) + (((int64_t)(vs - P2.y)) * ((int64_t)dy3));
            if ((dx3 < 0) || ((dx3 == 0) && (dy3 < 0))) dO3--; // top left rule (beware, changes total aera).
            O3 = (dO3 >= 0) ? ((int32_t)TGX_RASTERIZE_DIV256(dO3)) : -((int32_t)TGX_RASTERIZE_DIV256(-dO3 + (TGX_RASTERIZE_SUBPIXEL256 - 1)));
            }
 
        // beware that O1 + O2 + O3 = 0 is possible now but still we should not discard the triangle:
        // this case must be dealt with inside the shader...
        if (sx == 1)
            {
            while (((O1 | O2 | O3) < 0) && (sy > 0))
                {
                sy--;
                oy++;
                O1 += dy1;
                O2 += dy2;
                O3 += dy3;
                }
            if (sy == 0) return;
            }
        else if (sy == 1)
            {
            while (((O1 | O2 | O3) < 0) && (sx > 0))
                {
                sx--;
                ox++;
                O1 += dx1;
                O2 += dx2;
                O3 += dx3;
                }
            if (sx == 0) return;
            }
 
        const RasterizerVec4* F1 = &fP2;
        const RasterizerVec4* F2 = &V0;
        const RasterizerVec4* F3 = &fP1;
 
        if (dx1 <= 0)
            {
            if (dx2 > 0)
                {
                // Rotate left: edge2, edge3, edge1
                const int32_t tdx = dx1;
                const int32_t tdy = dy1;
                const int32_t tO  = O1;
                const RasterizerVec4* tF = F1;
 
                dx1 = dx2;
                dy1 = dy2;
                O1  = O2;
                F1  = F2;
 
                dx2 = dx3;
                dy2 = dy3;
                O2  = O3;
                F2  = F3;
 
                dx3 = tdx;
                dy3 = tdy;
                O3  = tO;
                F3  = tF;
                }
            else
                {
                // Rotate right: edge3, edge1, edge2
                const int32_t tdx = dx3;
                const int32_t tdy = dy3;
                const int32_t tO  = O3;
                const RasterizerVec4* tF = F3;
 
                dx3 = dx2;
                dy3 = dy2;
                O3  = O2;
                F3  = F2;
 
                dx2 = dx1;
                dy2 = dy1;
                O2  = O1;
                F2  = F1;
 
                dx1 = tdx;
                dy1 = tdy;
                O1  = tO;
                F1  = tF;
                }
            }
 
        shader_function(ox, oy, sx, sy, dx1, dy1, O1, *F1, dx2, dy2, O2, *F2, dx3, dy3, O3, *F3, data);
        
        return;
        }
 
 
 
 
 
 
 
    
}
 
#endif
 
#endif