Accuracy of Implicit Curve Rendering

ztlawton shared this problem 2 years ago

In Progress

I noticed that plotting the hyperbola eq1: x² + 2 / sqrt(3) x y - y² = 1 shows the x-intercepts at about -1.00000115 and 1.00000115 instead of exactly -1 and 1. Using the Intersect tool to show the intercept points Intersect(eq1, xAxis) correctly shows them at (-1, 0) and (1, 0), so that calculation is happening correctly behind the scenes, but something is going amiss with the display of the curve itself.

Plotting the same hyperbola as Curve((sqrt(1 / 2 sqrt(3) sec(2 (θ - π / 12))); θ), θ, 0, 2π) also works correctly, visually showing the x-intercepts at exactly -1 and 1, so the problem seems to be specifically with the implicit curve rendering rather than with the hyperbola itself.

I tested this in the web application and in the desktop program. Both showed the same problem.

The same problem

Comments (2)

Michael Borcherds ● 2 years ago

Thanks, we'll see if we can improve that.

You can also try

x + 2 / sqrt(3) y - y²/x = 1/x

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ztlawton ● 2 years ago

Interesting! That renders correctly. It also shows up in the Algebra panel as an Implicit Curve rather than as a Conic. Why does dividing the whole thing by x make that change?

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