S-curve Graph Mirror

[gcurl]

Hi All,

I have an s-curve equation that uses cosine. Any trigonometric function is allowed but I can't use exponential or logarithmic equations as they don't perform to what is required. The cosine equation works great for certain settings but for others, I need to mirror it using the existing coordinate points; I need to mirror the ess while using the same coordinate points. I've tried a few ways but I can't have the equation switching its location to a different quadrant. The attached mcad_pic1.png shows the equation, the current s-curve in red, and the needed s-curve in green. Please help me to find a variation of the current equation or a different trigonometric equation that will enable the green s-curve.

Thank you. Gary

[ValeryOchkov]

May by it help you?

[terryhendicott]

Hi,

Can you upload your worksheet?

Cheers

Terry

[ValeryOchkov]

Yes! We need the Mathcad 15 sheet - not the picture!

[terryhendicott]

Hi,

This function calculates the mirror point to point x,y about a line through two points x1,y1 and x2,y2.

You can use on x,b(x) coordinates to define the mirror graph.

Upload your sheet and I will show you how.

Cheers

Terry

[terryhendicott]

Hi,

Typed in the long equation and applied the function.

Cheers

Terry

[terryhendicott · Accepted solution]

Hi,

Sorry answer is so piecemeal.

The question was:

Please help me to find a variation of the current equation or a different trigonometric equation that will enable the green s-curve.

Function z(x) is the equation you are after

Cheers

Terry

[gcurl]

Dear Valery and Terry,

Thank you for your attention and I appreciate your expertise. Valery, your answer looks great but I, by myself, wouldn't be able to match it to my longer equation. Terry, yours works perfectly! Can either of you explain to me the theory behind this mirror effect? I studied both of your equations but nothing jumped out at me.

You both make the difficult look easy and I hope that everyone that reads this or any of your other posts understands your talents.

Thank you again. Gary

[terryhendicott]

Hi 

Can either of you explain to me the theory behind this mirror effect?

Have included some detail on how function z(x) was created in the enclosed worksheet.

This will explain the theory.

Cheers

Terry

[gcurl]

Thank you Terry,

I got lost in the cspline area as I have Mathcad 11. I viewed your file in SMath then copied it into 11. The cspline did not copy in SMath and there were some items, probably graphs and images, that did not work either. The text and the math did transfer.

I still, though, did not see how you got there. Your explanation was clear but I couldn't get it. I have a high IQ but apparently not high enough. Inverses and opposites are easy but this mirror at the coordinates gets away from me.

Kudos to you and much appreciation.

Gary

[gcurl]

Dear Terry and Valery,

I figured it out. Not the small details yet but, I see how you(Terry) used the first three segments of your equation to flip and scale it. The last two segments were obvious in their jobs. It matches to what Valery showed me in his smaller equation. I just have not dissected the first three segments yet.

Valery, I believe that Terry's method and your method are the same. At the time you initially posted your correct response, I was not learned enough yet to fully grasp what I eventually learned from Terry's response. I used your equation to teach myself about Terry's equation so you both were equally helpful; I used the easier one to teach the complex one.

Valery, I don't know how the Kudos operate here but I feel like you deserve one too!

Sincerely, Gary

[ttokoro]

Mirroring by rotaion of each point of red data.

[ttokoro]

Using VladimirN's 

Heart 2D in Mathcad 15 - PTC Community

[VladimirN]

😉