gallop={{3.444`,19.052`},{3.5`,18.753`},{3.662`,18.939`},{3.714`,18.577`},{3.495`,17.792`},{3.706`,18.08`},{3.811`,17.959`},{3.963`,18.122`},{3.832`,17.172`},{3.702`,17.27`},{4.428`,17.689`},{4.357`,17.073`},{4.229`,16.712`},{4.522`,15.402`},{4.722`,16.376`},{4.732`,16.015`},{4.833`,15.772`},{4.842`,15.935`},{4.885`,16.363`},{5.034`,16.881`},{5.078`,15.644`},{5.183`,15.644`},{5.247`,15.84`},{5.328`,15.358`},{5.328`,15.097`},{5.328`,14.871`},{5.328`,14.436`},{5.503`,15.729`},{5.558`,16.09`},{5.558`,15.378`},{5.558`,15.031`},{5.808`,15.916`},{5.775`,15.712`},{5.884`,14.588`},{6.03`,14.885`},{6.136`,16.322`},{6.176`,15.981`},{6.306`,15.893`},{6.367`,15.737`},{6.76`,15.22`}};

walk={{0.441`,27.776`},{0.519`,23.902`},{0.589`,22.941`},{0.645`,21.371`},{0.705`,19.966`},{0.767`,19.581`},{0.821`,17.873`},{0.98`,16.838`},{1.091`,15.37`},{1.209`,15.234`},{1.282`,15.334`},{1.363`,15.107`},{1.333`,15.891`},{1.19`,16.009`},{1.442`,16.556`},{1.578`,16.891`},{1.597`,17.58`},{1.613`,18.482`}};

trot={{1.142`,26.045`},{1.294`,25.022`},{1.223`,24.237`},{1.266`,22.623`},{1.257`,21.906`},{1.294`,21.842`},{1.33`,21.646`},{1.439`,21.119`},{1.566`,21.12`},{1.575`,20.692`},{1.494`,20.005`},{1.494`,19.522`},{1.711`,19.674`},{1.693`,19.169`},{1.865`,19.309`},{1.902`,18.913`},{1.709`,18.471`},{1.709`,17.921`},{1.727`,17.868`},{1.857`,17.868`},{1.958`,18.262`},{2.073`,18.097`},{2.027`,17.668`},{2.142`,17.218`},{2.142`,16.791`},{2.349`,16.891`},{2.445`,16.869`},{2.264`,15.72`},{2.292`,15.392`},{2.527`,15.14`},{2.618`,16.476`},{2.755`,14.88`},{2.9`,16.241`},{2.906`,16.043`},{3.045`,15.833`},{2.918`,15.159`},{3.016`,14.962`},{3.128`,15.06`},{3.259`,15.696`},{3.259`,14.927`},{3.25`,14.632`},{3.232`,14.349`},{3.226`,13.965`},{3.388`,13.081`},{3.338`,14.604`},{3.487`,14.604`},{3.478`,14.95`},{3.478`,15.262`},{3.666`,15.097`},{3.592`,14.666`},{3.707`,14.666`},{3.682`,14.081`},{3.64`,14.189`},{3.821`,13.835`},{3.938`,15.1`},{3.854`,15.54`},{3.826`,15.945`},{4.045`,15.326`},{4.178`,15.326`},{4.14`,15.734`},{4.183`,15.855`},{4.326`,15.887`},{4.326`,16.371`},{4.382`,16.5`},{4.382`,17.052`},{4.881`,16.789`},{5.104`,16.461`},{5.183`,17.235`},{4.996`,17.532`},{4.996`,18.117`},{5.246`,18.99`},{5.37`,17.955`}};

Wcurve={{0.388`,27.481`},{0.463`,24.849`},{0.594`,22.187`},{0.704`,20.328`},{0.816`,18.261`},{0.95`,16.729`},{1.034`,15.827`},{1.114`,15.254`},{1.184`,15.2`},{1.254`,15.265`},{1.358`,15.549`},{1.46`,16.024`},{1.522`,16.653`},{1.559`,17.504`},{1.593`,18.405`},{1.631`,19.207`},{1.674`,20.295`}};

Tcurve={{1.169`,25.906`},{1.25`,23.435`},{1.394`,21.11`},{1.641`,19.349`},{2.003`,17.605`},{2.423`,16.158`},{2.957`,14.967`},{3.199`,14.581`},{3.399`,14.449`},{3.588`,14.593`},{3.866`,15.031`},{4.288`,15.838`},{4.657`,16.698`},{5.31`,18.367`}};

Gcurve={{3.479`,18.669`},{3.91`,17.732`},{4.398`,16.903`},{4.908`,16.112`},{5.451`,15.596`},{5.795`,15.441`},{6.347`,15.379`},{6.698`,15.348`}};

wcurve=BezierFunction[Wcurve]
tcurve=BezierFunction[Tcurve]
gcurve=BezierFunction[Gcurve]

D[wcurve,t]

ListPlot[{walk,trot,gallop},PlotStyle->{Red,Blue,Green},PlotRange->{{0,7},{0,28}},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"},LabelStyle->Directive[FontSize->14]]

Export["1.eps",%371,"EPS"]

ListPlot[{walk,trot,gallop},PlotStyle->{Red,Blue,Green},PlotRange->{{0,7},{0,28}},AspectRatio->1]
ParametricPlot[{wcurve[t],tcurve[t],gcurve[t]},{t,0,1},PlotRange->{{0,7},{0,28}},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"},LabelStyle->Directive[FontSize->14],PlotStyle->{Red,Blue,Green}]
Show[%,%%]

Export["2.eps",%301,"EPS"]

ParametricPlot[{wcurve[t]},{t,0,.99},PlotRange->{{0,7},{0,28}},AspectRatio->1]
ParametricPlot[{tcurve[t]},{t,.21,.9},PlotRange->{{0,7},{0,28}},AspectRatio->1]
ParametricPlot[{gcurve[t]},{t,.34,1},PlotRange->{{0,7},{0,28}},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"},LabelStyle->Directive[FontSize->14]]
Show[%,%%,%%%]

ParametricPlot[{wcurve[t]},{t,0,.99},PlotRange->{{0,7},{0,28}},AspectRatio->1]
ParametricPlot[{tcurve[t]},{t,.21,.9},PlotRange->{{0,7},{0,28}},AspectRatio->1]
ParametricPlot[{gcurve[t]},{t,.34,1},PlotRange->{{0,7},{0,28}},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"},LabelStyle->Directive[FontSize->14]]
Show[%,%%,%%%]

Export["3.eps",%365,"EPS"]

1-.34

Differences[Table[wcurve[i][[1]],{i,0,.99,.01}]][[j]]

wdiff=Table[{Table[wcurve[i][[1]],{i,0,.99,.01}][[j]],((Differences[Table[wcurve[i][[2]],{i,0,.99,.01}]][[j]])/(Differences[Table[wcurve[i][[1]],{i,0,.99,.01}]][[j]]))},{j,1,99}];
tdiff=Table[{Table[tcurve[i][[1]],{i,.21,.9,.01}][[j]],((Differences[Table[tcurve[i][[2]],{i,.21,.9,.01}]][[j]])/(Differences[Table[tcurve[i][[1]],{i,.21,.9,.01}]][[j]]))},{j,1,69}];
gdiff=Table[{Table[gcurve[i][[1]],{i,.34,1,.01}][[j]],((Differences[Table[gcurve[i][[2]],{i,.34,1,.01}]][[j]])/(Differences[Table[gcurve[i][[1]],{i,.34,1,.01}]][[j]]))},{j,1,66}];

ListPlot[wdiff,Joined->True,AspectRatio->1,PlotRange->{{0,7},{-35,28}}]
ListPlot[tdiff,Joined->True,AspectRatio->1,PlotRange->{{0,7},{-35,28}}]
ListPlot[gdiff,Joined->True,AspectRatio->1,PlotRange->{{0,7},{-35,28}},Frame->True,FrameLabel->{"Running speed m/s","Change in oxygen consumption per change in speed (mL / m/s)"},LabelStyle->Directive[FontSize->14]]
Show[%,%%,%%%]

Export["1.eps",%24,"EPS"]

ListPlot[wdiff,Joined->True]

ListPlot[{walk,trot,gallop},PlotStyle->{Red,Blue,Green},PlotLegend->{"Walk","Trot","Gallop"},PlotRange->{{0,7},{0,28}},LegendPosition->{1,0},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"},ImageSize->500]

Epilog->ParametricPlot[{wcurve[t],tcurve[t],gcurve[t]},{t,0,1}]

Epilog->ParametricPlot[{wcurve[t],tcurve[t],gcurve[t]},{t,0,1},PlotStyle->{Red,Blue,Green},AspectRatio->1,PlotRange->{{0,7},{0,28}},Axes->False]

ParametricPlot[{wcurve[t],tcurve[t],gcurve[t]},{t,0,1},PlotStyle->{Red,Blue,Green},AspectRatio->1,PlotRange->{{0,7},{0,28}},Axes->False]

Overlay[{%187,%204}]

Show[ListPlot[{walk,trot,gallop},PlotStyle->{Red,Blue,Green},PlotLegend->{"Walk","Trot","Gallop"},PlotRange->{{0,7},{0,28}},LegendPosition->{1.1,-0.4},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"}],]

Show[{ParametricPlot[wcurve[t],{t,0,1}],ParametricPlot[tcurve[t],{t,0,1}],ParametricPlot[gcurve[t],{t,0,1}]},AspectRatio->1,PlotRange->{{0,7},{0,28}}]

Show[%,%%]

Show[{ParametricPlot[wcurve[t],{t,0,1}],ParametricPlot[tcurve[t],{t,0,1}],ParametricPlot[gcurve[t],{t,0,1}]},AspectRatio->1,PlotRange->{{0,7},{0,28}}]

Show[ParametricPlot[wcurve[t],{t,0,1}],ParametricPlot[tcurve[t],{t,0,1}],ParametricPlot[gcurve[t],{t,0,1}],PlotRange->{{0,7},{0,28}},AspectRatio->1,Frame->True,FrameLabel->{"Running speed m/s","mL oxygen consumed to move 1 meter"}]

Show[Graphics[{Red,Point[walk],Blue,Point[trot],Green,Point[gallop]},Axes->True],ParametricPlot[wcurve[t],{t,0,1}],ParametricPlot[tcurve[t],{t,0,1}],ParametricPlot[gcurve[t],{t,0,1}],PlotRange->{{0,7},{0,28}},AspectRatio->1]

ParametricPlot[{wcurve[t]},{t,0,.99},PlotRange->{{0,7},{0,28}},AspectRatio->1]

wdiff=Table[{Table[wcurve[i][[1]],{i,0,.99,.01}][[j]],Differences[Table[wcurve[i][[2]],{i,0,.99,.01}]][[j]]},{j,1,99}];

ListPlot[wdiff,Joined->True]

ListPlot[Differences[]]

ListPlot[Table[wcurve[i],{i,0,.99,.01}],Joined->True]