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畫線演算法 93610020 葉書豪 資工四

畫線演算法 93610020 葉書豪 資工四. Naive algoritm. A naïve line-drawing algorithm dx = x2 - x1//x 軸的間隔 dy = y2 - y1//y 軸的間隔 for x from x1 to x2 { y = y1 + (dy) * (x - x1)/(dx) plot(x, y) }// 從起始點根據斜率公式一點一點畫到終點 (dy) )/(dx) 即為協率. DDA algorithm. 根據 x 軸和 y 軸的增量來畫出一條線

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畫線演算法 93610020 葉書豪 資工四

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  1. 畫線演算法93610020 葉書豪 資工四

  2. Naivealgoritm • A naïve line-drawing algorithm dx = x2 - x1//x軸的間隔 dy = y2 - y1//y軸的間隔 for x from x1 to x2 { y = y1 + (dy) * (x - x1)/(dx) plot(x, y) }//從起始點根據斜率公式一點一點畫到終點 (dy) )/(dx)即為協率

  3. DDA algorithm • 根據x軸和y軸的增量來畫出一條線 x_incremennt = float(dx) / float(steps); y_incremennt = float(dy) / float(steps); 假如x的間距大於 y的間距 steps = fabs(dx); 不是的話 steps = fabs(dy); 這個演算法不是一個點一個點畫上去的 而是利用各+0.5的長度直線來趨近一條斜線

  4. Bresenhamalgorithm • Bresenham演算法對斜率介於0至1之間的直線繪製為(假設直線兩端點為(x,y)和(x,y), xx, yy)： • 輸入直線兩端點(x,y)及(x,y)。 • i=1; • Δx=x-x; Δy=y-y; P1=2Δy-Δx; (x1,y1)=(x,y); • Const1=2(Δx-Δy); Const2=-2Δy; • while (i≠Δx) { • if (Pi0) { • (xi+1,yi+1)=(xi+1,yi+1); • Pi+1=Pi+Const1; } • else { • (xi+1,yi+1)=(xi+1,yi); • Pi+1=Pi+Const2; } • i++; • } • 在此處2(Δx-Δy)和2Δy僅計算一次，其餘運算皆為整數的加減運算。 • 目前我們只討論斜率介於0和1之間的直線繪製，當直線斜率介於1至無窮大時，我們可經由增加yi之值(yi+1=yi+1)來求xi；

  5. 效率比較 • 基本上畫出來的 速度方面來上 都很快速 • 相差不遠 所以速度沒什麼影響 • 主要是線段的趨近方面 • Bresenham演算法會比較平順 • Naïve會比較一段一段的 而DDA演算法則比較粗一點 但是已經比較趨近線的平滑性了

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