对数螺线的编制
请大家帮忙，用VBA编制对数螺线，如何入手？对数螺线的极坐标方程为r=20exp(2*a)<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> ，r为极径，a为极角。<v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 47.25pt; HEIGHT: 18pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 47.25pt; HEIGHT: 18pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 47.25pt; HEIGHT: 18pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 47.25pt; HEIGHT: 18pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">其直角坐标方程为<o:p></o:p>
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<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt">图2对数螺线<o:p></o:p>
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</DIV></v:textbox></v:shape></v:group> y=20exp(2*a)*sina<v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 47.25pt; HEIGHT: 18pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 53.25pt; HEIGHT: 15.75pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape><o:p></o:p>
<v:group id=_x0000_s1026 style="MARGIN-TOP: 27.9pt; Z-INDEX: 1; LEFT: 0px; MARGIN-LEFT: 239.75pt; WIDTH: 142pt; POSITION: absolute; HEIGHT: 158.4pt; TEXT-ALIGN: left" coordsize="2840,3168" coordorigin="4897,10332"><v:group id=_x0000_s1027 style="LEFT: 4897px; WIDTH: 2840px; POSITION: absolute; TOP: 10332px; HEIGHT: 2779px" coordsize="2840,2779" coordorigin="1260,972"><v:shapetype id=_x0000_t5 path="m@0,l,21600r21600,xe" o:spt="5" coordsize="21600,21600" adj="10800"><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="prod #0 1 2"></v:f><v:f eqn="sum @1 10800 0"></v:f></v:formulas><v:path o:connecttype="custom" gradientshapeok="t" textboxrect="0,10800,10800,18000;5400,10800,16200,18000;10800,10800,21600,18000;0,7200,7200,21600;7200,7200,14400,21600;14400,7200,21600,21600" o:connectlocs="@0,0;@1,10800;0,21600;10800,21600;21600,21600;@2,10800"></v:path><v:handles><v:h xrange="0,21600" position="#0,topLeft"></v:h></v:handles></v:shapetype></v:group></v:group>
请大家多多指点！！谢谢了！！！<v:shape id=_x0000_i1026 style="WIDTH: 51pt; HEIGHT: 15.75pt" fillcolor="window" o:ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz"></v:imagedata></v:shape><v:shape id=_x0000_i1027 style="WIDTH: 9pt; HEIGHT: 17.25pt" fillcolor="window" o:ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\xxx\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz"></v:imagedata></v:shape> 这种只能通过模拟来生成曲线，比如间隔一定的角度算出这点的坐标，最后根据这些点生成多段线。 能用绘制样条曲线的方法编制吗?
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