Well, based on my very dusty old algebraic abilities, the conversion of Eq.2 to the trigonometric form yields: Then in the example which shows the core methodology/algorithm developed by the author, he claims that the above equation is equivalent to one written in complex numbers notation:į(t) = x(t) + iy(t) = exp(it) + exp(7it)/2 + exp(-17it)/3 Eq.2 The author claims that the first curve shown in Fig2. While entering formulas, I encountered some confusions in the article, something went wrong, hence the innocent project has had self-bloated to dangerous proportions. However, it took me much more time than I was originally expected. My aim was spending 0.25h to generate the curve you are interested in. Unfortunately, I have looked into the publication of the Mathematics and Computer Science of Santa Clara University by Frank A. The files are to be used for private, non-commercial purposes only. Download the files over a network, where the cost of doing so is not a concern. The stereo file requires an anaglyph red/ cyan glasses. For the best experience, use stand-alone media applications and the native resolution 3840x2160 – full screen. To be viewed on 4K media devices (monitors, UHD TVs, projectors.) of reasonable performance. TangoPetal_arcd.mp4 4K_stereo (170MB) link: TangoPetal_mono.mp4 4K_mono (60MB) link: Other coords systems in F360? Dreaming is free... so far. People would love it and study it extensively, I suppose. Not surprisingly, it is easy to conceptualize as it resembles a can of beer we are so fond of. The polar/cylindrical one would also be useful. In the mechanical world, which is staunchly conservative, the cartesian system suffices for most. On a side note, there are a vast number of specialized coordinate systems, particularly in higher dimensions (> 3D). ( Sin curve is so trivial that it is not attractive). In a general case, it is a little bit trickier process to accomplish.
Now, how to express it in polar coordinates?
In other cases, one could create even a quite complex in-sketch CAM mapping, ready to be used in subsequent steps of a design process. (I assume that a circle is defined in F360 by the standard parametric equation. In your particular case, the result would approximate sin-curve. Construct a fitted spline based on them.Ĩ. Collect index by index (x, y) coordinates pairs from both curves and draw the respective points.ħ. I think in the case of sin() parametric pattern on a curve should do the job, but another more sophisticated delineation is possible here.Ħ. On the circle (or an arbitrary curve) points positions will depend upon the mapping method, you desire. On the line segment, the placement of equidistant points would be preferable.ĥ. Place, on both curves an equal number of points.Ĥ. Draw a line segment from the circle centre (preferably X or Y axis parallel)ģ. Draw a circle (or any other curve, could be eg. As I am not at the front of a computer, the recipe will be in the verbose form.ġ. I would like you and others to consider the additional (not necessary time saving) method. Well, this has been pointed out by other interlocutors of this post. One obvious way to overcome this is to substitute the parent/grandparent with the common universal template, spline that is. It’s the norm in contemporary society, so there is no point to complain. Drawing the perfect sin-curve is not facilitated by F360 interface, although it’s 2D&3D descendant are.