When I want to move object around point I do:
point.x *= cosf(timer.timeElapsed);
point.y *= sinf(timer.timeElapsed);
How to make point move on eight or infinity sign trajectory?
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4 Answers
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2\$\begingroup\$ Answers should be self-contained, external links may die some day and would render this answer useless. You should quote the important bits from the links you've provided. \$\endgroup\$– Brian H.Dec 21, 2017 at 10:09
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As Marton notes, there are several "figure of eight" curves that might fit your needs. Perhaps the simplest is the lemniscate of Gerono, which has the parametrization:
x = cos(t);
y = sin(2*t) / 2;
and looks like this:
However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2*t)):
scale = 2 / (3 - cos(2*t));
x = scale * cos(t);
y = scale * sin(2*t) / 2;
It looks like this:
(Animations made with Maple 13, compressed with GIFsicle.)
answered Nov 13, 2012 at 14:36
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\$\begingroup\$ Thank you, everybody, for your support, which has earned me my first gold badge here on gamedev! :-) \$\endgroup\$ Nov 13, 2012 at 23:07
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1\$\begingroup\$ +1 for not only posting the links, but also the formulas and graphics ( with sources ). \$\endgroup\$ Nov 14, 2012 at 7:54
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2\$\begingroup\$ As is, this should be the accepted answer. \$\endgroup\$– Brian H.Dec 21, 2017 at 10:09
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I randomly found another one using this formula:
$$x^2 = y^2 + 0.1x^{2.8}$$
As plotted by Wolfram Alpha:
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\$\begingroup\$ Unlike the other answers, this one is currently not presented in parametric form that lets us easily step the position forward over time
t. I'd recommend including a description of how you would use this formula to position a moving object over time. \$\endgroup\$– DMGregory ♦Dec 21, 2017 at 14:11
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$$((x+1)^2+y^2)((x-1)^2+y^2)=1$$
The product of the distances from any point on that curve to (-1, 0) and to (1,0) is constant and equals to 1.
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4\$\begingroup\$ This answer provides a formula modelling such a curve, but not a method to "move an object" in such a way that it follows that curve. Please consider elaborating on the answer to indicate how you would use this math to move an object in a game. \$\endgroup\$– DMGregory ♦Jan 13, 2018 at 23:30