--- motion_comp.c 2002/03/08 02:44:50 1.1 +++ motion_comp.c 2003/01/03 12:43:38 1.11.2.18 @@ -1,147 +1,438 @@ +// 30.10.2002 corrected qpel chroma rounding +// 04.10.2002 added qpel support to MBMotionCompensation +// 01.05.2002 updated MBMotionCompensationBVOP +// 14.04.2002 bframe compensation + #include "../encoder.h" #include "../utils/mbfunctions.h" #include "../image/interpolate8x8.h" +#include "../image/reduced.h" #include "../utils/timer.h" +#include "motion.h" + +static __inline void +compensate16x16_interpolate(int16_t * const dct_codes, + uint8_t * const cur, + const uint8_t * const ref, + const uint8_t * const refh, + const uint8_t * const refv, + const uint8_t * const refhv, + uint8_t * const tmp, + uint32_t x, + uint32_t y, + const int32_t dx, + const int32_t dy, + const uint32_t stride, + const int quarterpel, + const int reduced_resolution, + const uint32_t rounding) +{ + const uint8_t * ptr; + + if (!reduced_resolution) { + + if(quarterpel) { + if (dx&3 | dy&3) { + interpolate16x16_quarterpel(tmp - y * stride - x, + (uint8_t *) ref, tmp + 32, + tmp + 64, tmp + 96, x, y, dx, dy, stride, rounding); + ptr = tmp; + } else ptr = ref + (y + dy/4)*stride + x + dx/4; // fullpixel position + + } else ptr = get_ref(ref, refh, refv, refhv, x, y, 1, dx, dy, stride); + + transfer_8to16sub(dct_codes, cur + y * stride + x, + ptr, stride); + transfer_8to16sub(dct_codes+64, cur + y * stride + x + 8, + ptr + 8, stride); + transfer_8to16sub(dct_codes+128, cur + y * stride + x + 8*stride, + ptr + 8*stride, stride); + transfer_8to16sub(dct_codes+192, cur + y * stride + x + 8*stride+8, + ptr + 8*stride + 8, stride); + + } else { //reduced_resolution + + x *= 2; y *= 2; + + ptr = get_ref(ref, refh, refv, refhv, x, y, 1, dx, dy, stride); + + filter_18x18_to_8x8(dct_codes, cur+y*stride + x, stride); + filter_diff_18x18_to_8x8(dct_codes, ptr, stride); + + filter_18x18_to_8x8(dct_codes+64, cur+y*stride + x + 16, stride); + filter_diff_18x18_to_8x8(dct_codes+64, ptr + 16, stride); -#define ABS(X) (((X)>0)?(X):-(X)) -#define SIGN(X) (((X)>0)?1:-1) + filter_18x18_to_8x8(dct_codes+128, cur+(y+16)*stride + x, stride); + filter_diff_18x18_to_8x8(dct_codes+128, ptr + 16*stride, stride); -static __inline void compensate8x8_halfpel( - int16_t * const dct_codes, - uint8_t * const cur, - const uint8_t * const ref, - const uint8_t * const refh, - const uint8_t * const refv, - const uint8_t * const refhv, - const uint32_t x, const uint32_t y, - const int32_t dx, const int dy, - const uint32_t stride) + filter_18x18_to_8x8(dct_codes+192, cur+(y+16)*stride + x + 16, stride); + filter_diff_18x18_to_8x8(dct_codes+192, ptr + 16*stride + 16, stride); + + transfer32x32_copy(cur + y*stride + x, ptr, stride); + } +} + +static __inline void +compensate8x8_interpolate( int16_t * const dct_codes, + uint8_t * const cur, + const uint8_t * const ref, + const uint8_t * const refh, + const uint8_t * const refv, + const uint8_t * const refhv, + uint8_t * const tmp, + uint32_t x, + uint32_t y, + const int32_t dx, + const int32_t dy, + const uint32_t stride, + const uint32_t quarterpel, + const int reduced_resolution, + const uint32_t rounding) { - int32_t ddx,ddy; + const uint8_t * ptr; - switch ( ((dx&1)<<1) + (dy&1) ) // ((dx%2)?2:0)+((dy%2)?1:0) - { - case 0 : - ddx = dx/2; - ddy = dy/2; - transfer_8to16sub(dct_codes, cur + y*stride + x, - ref + (y+ddy)*stride + x+ddx, stride); - break; + if (!reduced_resolution) { - case 1 : - ddx = dx/2; - ddy = (dy-1)/2; - transfer_8to16sub(dct_codes, cur + y*stride + x, - refv + (y+ddy)*stride + x+ddx, stride); - break; + if(quarterpel) { + if (dx&3 | dy&3) { + interpolate8x8_quarterpel(tmp - y*stride - x, + (uint8_t *) ref, tmp + 32, + tmp + 64, tmp + 96, x, y, dx, dy, stride, rounding); + ptr = tmp; + } else ptr = ref + (y + dy/4)*stride + x + dx/4; // fullpixel position + } else ptr = get_ref(ref, refh, refv, refhv, x, y, 1, dx, dy, stride); - case 2 : - ddx = (dx-1)/2; - ddy = dy/2; - transfer_8to16sub(dct_codes, cur + y*stride + x, - refh + (y+ddy)*stride + x+ddx, stride); - break; + transfer_8to16sub(dct_codes, cur + y * stride + x, ptr, stride); - default : // case 3: - ddx = (dx-1)/2; - ddy = (dy-1)/2; - transfer_8to16sub(dct_codes, cur + y*stride + x, - refhv + (y+ddy)*stride + x+ddx, stride); - break; - } + } else { //reduced_resolution + + x *= 2; y *= 2; + + ptr = get_ref(ref, refh, refv, refhv, x, y, 1, dx, dy, stride); + + filter_18x18_to_8x8(dct_codes, cur+y*stride + x, stride); + filter_diff_18x18_to_8x8(dct_codes, ptr, stride); + + transfer16x16_copy(cur + y*stride + x, ptr, stride); + } } +/* XXX: slow, inelegant... */ +static void +interpolate18x18_switch(uint8_t * const cur, + const uint8_t * const refn, + const uint32_t x, + const uint32_t y, + const int32_t dx, + const int dy, + const uint32_t stride, + const uint32_t rounding) +{ + interpolate8x8_switch(cur, refn, x-1, y-1, dx, dy, stride, rounding); + interpolate8x8_switch(cur, refn, x+7, y-1, dx, dy, stride, rounding); + interpolate8x8_switch(cur, refn, x+9, y-1, dx, dy, stride, rounding); + + interpolate8x8_switch(cur, refn, x-1, y+7, dx, dy, stride, rounding); + interpolate8x8_switch(cur, refn, x+7, y+7, dx, dy, stride, rounding); + interpolate8x8_switch(cur, refn, x+9, y+7, dx, dy, stride, rounding); + + interpolate8x8_switch(cur, refn, x-1, y+9, dx, dy, stride, rounding); + interpolate8x8_switch(cur, refn, x+7, y+9, dx, dy, stride, rounding); + interpolate8x8_switch(cur, refn, x+9, y+9, dx, dy, stride, rounding); +} +static void +CompensateChroma( int dx, int dy, + const int i, const int j, + IMAGE * const Cur, + const IMAGE * const Ref, + uint8_t * const temp, + int16_t * const coeff, + const uint32_t stride, + const int rounding, + const int rrv) +{ /* uv-block-based compensation */ + + if (!rrv) { + transfer_8to16sub(coeff, Cur->u + 8 * j * stride + 8 * i, + interpolate8x8_switch2(temp, Ref->u, 8 * i, 8 * j, + dx, dy, stride, rounding), + stride); + + transfer_8to16sub(coeff + 64, Cur->v + 8 * j * stride + 8 * i, + interpolate8x8_switch2(temp, Ref->v, 8 * i, 8 * j, + dx, dy, stride, rounding), + stride); + } else { + uint8_t * current, * reference; + + current = Cur->u + 16*j*stride + 16*i; + reference = temp - 16*j*stride - 16*i; + interpolate18x18_switch(reference, Ref->u, 16*i, 16*j, dx, dy, stride, rounding); + filter_18x18_to_8x8(coeff, current, stride); + filter_diff_18x18_to_8x8(coeff, temp, stride); + transfer16x16_copy(current, temp, stride); + + current = Cur->v + 16*j*stride + 16*i; + interpolate18x18_switch(reference, Ref->v, 16*i, 16*j, dx, dy, stride, rounding); + filter_18x18_to_8x8(coeff + 64, current, stride); + filter_diff_18x18_to_8x8(coeff + 64, temp, stride); + transfer16x16_copy(current, temp, stride); + } +} + +void +MBMotionCompensation(MACROBLOCK * const mb, + const uint32_t i, + const uint32_t j, + const IMAGE * const ref, + const IMAGE * const refh, + const IMAGE * const refv, + const IMAGE * const refhv, + IMAGE * const cur, + int16_t * dct_codes, + const uint32_t width, + const uint32_t height, + const uint32_t edged_width, + const int quarterpel, + const int reduced_resolution, + const uint32_t rounding) +{ + int32_t dx = (quarterpel ? mb->qmvs[0].x : mb->mvs[0].x); + int32_t dy = (quarterpel ? mb->qmvs[0].y : mb->mvs[0].y); + uint8_t * const tmp = refv->u; + + if ( mb->mode == MODE_NOT_CODED && dx==0 && dy==0 && !reduced_resolution) { /* quick copy */ + transfer16x16_copy(cur->y + 16 * (i + j * edged_width), + ref->y + 16 * (i + j * edged_width), + edged_width); + + transfer8x8_copy(cur->u + 8 * (i + j * edged_width/2), + ref->u + 8 * (i + j * edged_width/2), + edged_width / 2); + transfer8x8_copy(cur->v + 8 * (i + j * edged_width/2), + ref->v + 8 * (i + j * edged_width/2), + edged_width / 2); + return; + } + + if ((mb->mode == MODE_NOT_CODED || mb->mode == MODE_INTER || mb->mode == MODE_INTER_Q) /*&& !quarterpel*/) { + + /* quick MODE_NOT_CODED for GMC with MV!=(0,0) is still needed */ + + if (reduced_resolution) { + dx = RRV_MV_SCALEUP(dx); + dy = RRV_MV_SCALEUP(dy); + } + + compensate16x16_interpolate(&dct_codes[0 * 64], cur->y, ref->y, refh->y, + refv->y, refhv->y, tmp, 16 * i, 16 * j, dx, dy, + edged_width, quarterpel, reduced_resolution, rounding); + + dx /= 1 + quarterpel; + dy /= 1 + quarterpel; + dx = (dx >> 1) + roundtab_79[dx & 0x3]; + dy = (dy >> 1) + roundtab_79[dy & 0x3]; + + } else { // mode == MODE_INTER4V + int k, sumx = 0, sumy = 0; + const VECTOR * const mvs = (quarterpel ? mb->qmvs : mb->mvs); + + for (k = 0; k < 4; k++) { + dx = mvs[k].x; + dy = mvs[k].y; + sumx += dx / (1 + quarterpel); + sumy += dy / (1 + quarterpel); + + if (reduced_resolution){ + dx = RRV_MV_SCALEUP(dx); + dy = RRV_MV_SCALEUP(dy); + } + + compensate8x8_interpolate(&dct_codes[k * 64], cur->y, ref->y, refh->y, + refv->y, refhv->y, tmp, 16 * i + 8*(k&1), 16 * j + 8*(k>>1), dx, + dy, edged_width, quarterpel, reduced_resolution, rounding); + } + dx = (sumx >> 3) + roundtab_76[sumx & 0xf]; + dy = (sumy >> 3) + roundtab_76[sumy & 0xf]; + } -void MBMotionCompensation( - MACROBLOCK * const mb, - const uint32_t i, - const uint32_t j, - const IMAGE * const ref, - const IMAGE * const refh, - const IMAGE * const refv, - const IMAGE * const refhv, - IMAGE * const cur, - int16_t dct_codes[][64], - const uint32_t width, - const uint32_t height, - const uint32_t edged_width, - const uint32_t rounding) + CompensateChroma(dx, dy, i, j, cur, ref, tmp, + &dct_codes[4 * 64], edged_width / 2, rounding, reduced_resolution); + +} + + +void +MBMotionCompensationBVOP(MBParam * pParam, + MACROBLOCK * const mb, + const uint32_t i, + const uint32_t j, + IMAGE * const cur, + const IMAGE * const f_ref, + const IMAGE * const f_refh, + const IMAGE * const f_refv, + const IMAGE * const f_refhv, + const IMAGE * const b_ref, + const IMAGE * const b_refh, + const IMAGE * const b_refv, + const IMAGE * const b_refhv, + int16_t * dct_codes) { - static const uint32_t roundtab[16] = - { 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2 }; + const uint32_t edged_width = pParam->edged_width; + int32_t dx, dy, b_dx, b_dy, sumx, sumy, b_sumx, b_sumy; + int k; + const int quarterpel = pParam->m_quarterpel; + const uint8_t * ptr1, * ptr2; + uint8_t * const tmp = f_refv->u; + const VECTOR * const fmvs = (quarterpel ? mb->qmvs : mb->mvs); + const VECTOR * const bmvs = (quarterpel ? mb->b_qmvs : mb->b_mvs); + + switch (mb->mode) { + case MODE_FORWARD: + dx = fmvs->x; dy = fmvs->y; + + compensate16x16_interpolate(&dct_codes[0 * 64], cur->y, f_ref->y, f_refh->y, + f_refv->y, f_refhv->y, tmp, 16 * i, 16 * j, dx, + dy, edged_width, quarterpel, 0, 0); + + dx /= 1 + quarterpel; + dy /= 1 + quarterpel; + CompensateChroma( (dx >> 1) + roundtab_79[dx & 0x3], + (dy >> 1) + roundtab_79[dy & 0x3], + i, j, cur, f_ref, tmp, + &dct_codes[4 * 64], edged_width / 2, 0, 0); + + return; + + case MODE_BACKWARD: + b_dx = bmvs->x; b_dy = bmvs->y; + + compensate16x16_interpolate(&dct_codes[0 * 64], cur->y, b_ref->y, b_refh->y, + b_refv->y, b_refhv->y, tmp, 16 * i, 16 * j, b_dx, + b_dy, edged_width, quarterpel, 0, 0); + + b_dx /= 1 + quarterpel; + b_dy /= 1 + quarterpel; + CompensateChroma( (b_dx >> 1) + roundtab_79[b_dx & 0x3], + (b_dy >> 1) + roundtab_79[b_dy & 0x3], + i, j, cur, b_ref, tmp, + &dct_codes[4 * 64], edged_width / 2, 0, 0); + + return; + + case MODE_INTERPOLATE: /* _could_ use DIRECT, but would be overkill (no 4MV there) */ + case MODE_DIRECT_NO4V: + dx = fmvs->x; dy = fmvs->y; + b_dx = bmvs->x; b_dy = bmvs->y; + + if (quarterpel) { + + if (dx&3 | dy&3) { + interpolate16x16_quarterpel(tmp - i * 16 - j * 16 * edged_width, + (uint8_t *) f_ref->y, tmp + 32, + tmp + 64, tmp + 96, 16*i, 16*j, dx, dy, edged_width, 0); + ptr1 = tmp; + } else ptr1 = f_ref->y + (16*j + dy/4)*edged_width + 16*i + dx/4; // fullpixel position + + if (b_dx&3 | b_dy&3) { + interpolate16x16_quarterpel(tmp - i * 16 - j * 16 * edged_width + 16, + (uint8_t *) b_ref->y, tmp + 32, + tmp + 64, tmp + 96, 16*i, 16*j, b_dx, b_dy, edged_width, 0); + ptr2 = tmp + 16; + } else ptr2 = b_ref->y + (16*j + b_dy/4)*edged_width + 16*i + b_dx/4; // fullpixel position + + b_dx /= 2; + b_dy /= 2; + dx /= 2; + dy /= 2; + + } else { + ptr1 = get_ref(f_ref->y, f_refh->y, f_refv->y, f_refhv->y, + i, j, 16, dx, dy, edged_width); + + ptr2 = get_ref(b_ref->y, b_refh->y, b_refv->y, b_refhv->y, + i, j, 16, b_dx, b_dy, edged_width); + } + for (k = 0; k < 4; k++) + transfer_8to16sub2(&dct_codes[k * 64], + cur->y + (i * 16+(k&1)*8) + (j * 16+((k>>1)*8)) * edged_width, + ptr1 + (k&1)*8 + (k>>1)*8*edged_width, + ptr2 + (k&1)*8 + (k>>1)*8*edged_width, edged_width); + + dx = (dx >> 1) + roundtab_79[dx & 0x3]; + dy = (dy >> 1) + roundtab_79[dy & 0x3]; - if (mb->mode == MODE_INTER || mb->mode == MODE_INTER_Q) - { - int32_t dx = mb->mvs[0].x; - int32_t dy = mb->mvs[0].y; - - compensate8x8_halfpel(dct_codes[0], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i, 16*j, dx, dy, edged_width); - compensate8x8_halfpel(dct_codes[1], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i + 8, 16*j, dx, dy, edged_width); - compensate8x8_halfpel(dct_codes[2], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i, 16*j + 8, dx, dy, edged_width); - compensate8x8_halfpel(dct_codes[3], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i + 8, 16*j + 8, dx, dy, edged_width); - - dx = (dx & 3) ? (dx >> 1) | 1 : dx / 2; - dy = (dy & 3) ? (dy >> 1) | 1 : dy / 2; - - /* uv-image-based compensation - compensate8x8_halfpel(dct_codes[4], cur->u, ref->u, refh->u, refv->u, refhv->u, - 8*i, 8*j, dx, dy, edged_width/2); - compensate8x8_halfpel(dct_codes[5], cur->v, ref->v, refh->v, refv->v, refhv->v, - 8*i, 8*j, dx, dy, edged_width/2); */ - - /* uv-block-based compensation */ - interpolate8x8_switch(refv->u, ref->u, 8*i, 8*j, dx, dy, edged_width/2, rounding); - transfer_8to16sub(dct_codes[4], - cur->u + 8*j*edged_width/2 + 8*i, - refv->u + 8*j*edged_width/2 + 8*i, edged_width/2); - - interpolate8x8_switch(refv->v, ref->v, 8*i, 8*j, dx, dy, edged_width/2, rounding); - transfer_8to16sub(dct_codes[5], - cur->v + 8*j*edged_width/2 + 8*i, - refv->v + 8*j*edged_width/2 + 8*i, edged_width/2); - - } - else // mode == MODE_INTER4V - { - int32_t sum, dx, dy; - - compensate8x8_halfpel(dct_codes[0], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i, 16*j, mb->mvs[0].x, mb->mvs[0].y, edged_width); - compensate8x8_halfpel(dct_codes[1], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i + 8, 16*j, mb->mvs[1].x, mb->mvs[1].y, edged_width); - compensate8x8_halfpel(dct_codes[2], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i, 16*j + 8, mb->mvs[2].x, mb->mvs[2].y, edged_width); - compensate8x8_halfpel(dct_codes[3], cur->y, ref->y, refh->y, refv->y, refhv->y, - 16*i + 8, 16*j + 8, mb->mvs[3].x, mb->mvs[3].y, edged_width); - - sum = mb->mvs[0].x + mb->mvs[1].x + mb->mvs[2].x + mb->mvs[3].x; - dx = (sum ? SIGN(sum) * (roundtab[ABS(sum) % 16] + (ABS(sum) / 16) * 2) : 0); - - sum = mb->mvs[0].y + mb->mvs[1].y + mb->mvs[2].y + mb->mvs[3].y; - dy = (sum ? SIGN(sum) * (roundtab[ABS(sum) % 16] + (ABS(sum) / 16) * 2) : 0); - - /* uv-image-based compensation - compensate8x8_halfpel(dct_codes[4], cur->u, ref->u, refh->u, refv->u, refhv->u, - 8*i, 8*j, dx, dy, edged_width/2); - compensate8x8_halfpel(dct_codes[5], cur->v, ref->v, refh->v, refv->v, refhv->v, - 8*i, 8*j, dx, dy, edged_width/2); */ - - /* uv-block-based compensation */ - interpolate8x8_switch(refv->u, ref->u, 8*i, 8*j, dx, dy, edged_width/2, rounding); - transfer_8to16sub(dct_codes[4], - cur->u + 8*j*edged_width/2 + 8*i, - refv->u + 8*j*edged_width/2 + 8*i, edged_width/2); - - interpolate8x8_switch(refv->v, ref->v, 8*i, 8*j, dx, dy, edged_width/2, rounding); - transfer_8to16sub(dct_codes[5], - cur->v + 8*j*edged_width/2 + 8*i, - refv->v + 8*j*edged_width/2 + 8*i, edged_width/2); + b_dx = (b_dx >> 1) + roundtab_79[b_dx & 0x3]; + b_dy = (b_dy >> 1) + roundtab_79[b_dy & 0x3]; + break; + + default: // MODE_DIRECT + sumx = sumy = b_sumx = b_sumy = 0; + + for (k = 0; k < 4; k++) { + + dx = fmvs[k].x; dy = fmvs[k].y; + b_dx = bmvs[k].x; b_dy = bmvs[k].y; + + if (quarterpel) { + sumx += dx/2; sumy += dy/2; + b_sumx += b_dx/2; b_sumy += b_dy/2; + + if (dx&3 | dy&3) { + interpolate8x8_quarterpel(tmp - (i * 16+(k&1)*8) - (j * 16+((k>>1)*8)) * edged_width, + (uint8_t *) f_ref->y, + tmp + 32, tmp + 64, tmp + 96, + 16*i + (k&1)*8, 16*j + (k>>1)*8, dx, dy, edged_width, 0); + ptr1 = tmp; + } else ptr1 = f_ref->y + (16*j + (k>>1)*8 + dy/4)*edged_width + 16*i + (k&1)*8 + dx/4; + + if (b_dx&3 | b_dy&3) { + interpolate8x8_quarterpel(tmp - (i * 16+(k&1)*8) - (j * 16+((k>>1)*8)) * edged_width + 16, + (uint8_t *) b_ref->y, + tmp + 16, tmp + 32, tmp + 48, + 16*i + (k&1)*8, 16*j + (k>>1)*8, b_dx, b_dy, edged_width, 0); + ptr2 = tmp + 16; + } else ptr2 = b_ref->y + (16*j + (k>>1)*8 + b_dy/4)*edged_width + 16*i + (k&1)*8 + b_dx/4; + } else { + sumx += dx; sumy += dy; + b_sumx += b_dx; b_sumy += b_dy; + + ptr1 = get_ref(f_ref->y, f_refh->y, f_refv->y, f_refhv->y, + 2*i + (k&1), 2*j + (k>>1), 8, dx, dy, edged_width); + ptr2 = get_ref(b_ref->y, b_refh->y, b_refv->y, b_refhv->y, + 2*i + (k&1), 2*j + (k>>1), 8, b_dx, b_dy, edged_width); + } + transfer_8to16sub2(&dct_codes[k * 64], + cur->y + (i * 16+(k&1)*8) + (j * 16+((k>>1)*8)) * edged_width, + ptr1, ptr2, edged_width); + + } + + dx = (sumx >> 3) + roundtab_76[sumx & 0xf]; + dy = (sumy >> 3) + roundtab_76[sumy & 0xf]; + b_dx = (b_sumx >> 3) + roundtab_76[b_sumx & 0xf]; + b_dy = (b_sumy >> 3) + roundtab_76[b_sumy & 0xf]; + + break; } + + // uv block-based chroma interpolation for direct and interpolate modes + transfer_8to16sub2(&dct_codes[4 * 64], + cur->u + (j * 8) * edged_width / 2 + (i * 8), + interpolate8x8_switch2(tmp, b_ref->u, 8 * i, 8 * j, + b_dx, b_dy, edged_width / 2, 0), + interpolate8x8_switch2(tmp + 8, f_ref->u, 8 * i, 8 * j, + dx, dy, edged_width / 2, 0), + edged_width / 2); + + transfer_8to16sub2(&dct_codes[5 * 64], + cur->v + (j * 8) * edged_width / 2 + (i * 8), + interpolate8x8_switch2(tmp, b_ref->v, 8 * i, 8 * j, + b_dx, b_dy, edged_width / 2, 0), + interpolate8x8_switch2(tmp + 8, f_ref->v, 8 * i, 8 * j, + dx, dy, edged_width / 2, 0), + edged_width / 2); }