Hi, First, find the actual point along the curve of the wave you want, then you can ask for the direction of the wave at that time, and its point: \startuseMPgraphic{Waves} numeric height,stops,yoffset; stops := 10; height := OverlayHeight/10; path wave[]; % storing waves draw (0,0)--(OverlayWidth,0)--(OverlayWidth,OverlayHeight) withcolor white withpen pencircle scaled 0.01; for j=1 upto 3: definecolor [name="Sea", y=(j/20), c=2*(j/10), m=(j/20)]; yoffset := height/(j*2); wave[j] := (0,0)--(0,yoffset)... for i=1 upto stops: (OverlayWidth*i/(stops+1), (yoffset) randomized (height/2)) ... endfor (OverlayWidth,yoffset); fill ((0,0)--wave[j]--(OverlayWidth,0)--cycle) withcolor "Sea"; endfor; xpos := OverlayWidth * RealPageNumber/NOfPages; path ship; ship := (0,10)---(70,10)...(60,0)---(10,0)...cycle; pair itime, iangle, boatpos; itime = (wave[3] intersectiontimes ((xpos,0)--(xpos,infinity))); iangle = direction (xpart itime) of wave[3]; boatpos = (point (xpart itime) of wave[3]) shifted (-5,0); % shift to center horizontally fill ship xysized (10,5) shifted boatpos rotatedaround (boatpos, angle iangle) withcolor red; \stopuseMPgraph

On 19 Jul 2023, at 12:32, Henning Hraban Ramm wrote:

Hi, I’d like a presentation progress indicator that looks like a boat on waves – and if it works, it can also become a bike on hills or a mars rover on dunes. But my math skills are lacking.

Below’s a mostly working draft.

* I find the waves not yet very convincing. Would it make sense to use a randomized sinus? (How?)

* The boat should sit on the middle wave and be rotated by the current slope. I know I need the “time” of the upper curve and get the 1st derivation, but how?

""" \setuppapersize[SW]

\startuseMPgraphic{Waves} numeric height,stops,yoffset; stops := 10; height := OverlayHeight/10; path wave;

draw (0,0)--(OverlayWidth,0)--(OverlayWidth,OverlayHeight) withcolor white withpen pencircle scaled 0.01;

for j=1 upto 3: definecolor [name="Sea", y=(j/20), c=2*(j/10), m=(j/20)]; yoffset := height/(j*2); wave := (0,0)--(0,yoffset)... for i=1 upto stops: (OverlayWidth*i/(stops+1), (yoffset) randomized (height/2)) ... endfor (OverlayWidth,yoffset)--(OverlayWidth,0)--cycle; fill wave withcolor "Sea"; endfor;

pair pos; pos := (OverlayWidth * RealPageNumber/NOfPages, height/2 randomized 2); path ship; ship := (0,10)---(70,10)...(60,0)---(10,0)...cycle;

fill ship xysized (10,5) shifted pos rotatedaround (pos, 15) withcolor red; \stopuseMPgraphic

\defineoverlay[Waves][\useMPgraphic{Waves}]

\setupbackgrounds[state=repeat] \setupbackgrounds[page][background={Waves}]

\starttext

\dorecurse{10}{\recurselevel\page}

\stoptext """

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