Bresenham高效画线算法
画线的算法不少，但要作到高速、简单并不容易。斜率相乘法是最简单的方法之一，但计算每个点均要花费不少时间用于乘、除法运算；下面介绍的是Bresenham's高效画线算法，对每个点的坐标计算只要加、减法就能完成。 简化算法用伪Pascal语言描述如下：procedure DrawLine(x1, y1, x2, y2: Integer);var x, y, DeltaX, DeltaY, HalfX, ErrorTerm, i: Integer;begin DeltaX := x2 - x1; DeltaY := y2 - y1; HalfX := (x2 - x1) shr 1; ErrorTerm := 0; x := x1; y := y1; for i:=0 to DeltaX do begin Plot(X, Y); Inc(x); ErrorTerm := ErrorTerm + DeltaY; if ErrorTerm>HalfX then begin ErrorTerm := ErrorTerm - DeltaX; Inc(y); end; end;end; 为方便阅读，上述程序作了简化。实际程序应略作修正，以分别处理DeltaX与DeltaY比较大小, 必要时交换起始、结束点等。 修正后的的伪Pascal算法如下：procedure DrawLine(x1, y1, x2, y2: Integer);var x, y, DeltaX, DeltaY, HalfCount, ErrorTerm, i, Flag: Integer;begin DeltaX := x2 - x1; DeltaY := y2 - y1;
if Abs(DeltaY)<Abs(DeltaX) then begin if DeltaX<0 then begin i := x1; x1 := x2; x2 := i; i := y1; y1 := y2; y2 := i; DeltaX := x2 - x1; DeltaY := y2 - y1; end; if DeltaY<0 then Flag := -1 else Flag := 1; DeltaY := Abs(DeltaY); HalfCount := DeltaX shr 1; ErrorTerm := 0; x := x1; y := y1; for i:=0 to DeltaX do begin Plot(X, Y); Inc(x); ErrorTerm := ErrorTerm + DeltaY; if ErrorTerm>HalfCount then begin ErrorTerm := ErrorTerm - DeltaX; y := y + Flag; end; end; end else begin if DeltaY<0 then begin i := x1; x1 := x2; x2 := i; i := y1; y1 := y2; y2 := i; DeltaX := x2 - x1; DeltaY := y2 - y1; end; if DeltaX<0 then Flag := -1 else Flag := 1; DeltaX := Abs(DeltaX); HalfCount := DeltaY shr 1; ErrorTerm := 0; x := x1; y := y1; for i:=0 to DeltaY do begin Plot(X, Y); Inc(y); ErrorTerm := ErrorTerm + DeltaX; if ErrorTerm>HalfCount then begin ErrorTerm := ErrorTerm - DeltaY; x := x + Flag; end; end; end;end;
