I am trying to work with a parametric equation, and I have been out of college for several years so please bear with me.
I have this curve I have worked forever to find an equation for, and it begins at (0,0) and the line that goes from end to end is equal with the x axis, so its midpoint crosses the x axis, and its end point lies on the x axis.
i found the equation to the curve as a cubic bezier equation. My question is this: the original equation has a line from end to end with slope of 0. But what if I need to move the curve around, so as the beginning of the curve starts at lets say (5,2) and the slope of the line from end to end is now changed?
I want to be able to move my curve around the board so to speak, and be able to find the range of date that the curve contains each time i move it. How would this change my original equation? do I need to find a new equation each time my beginning, middle and end points change, even though the curve proportion remains the same?
I hope this makes sense. Thanks in advance for your help.
If you know that your parametric equation is a cubic Bezier curve, you must have the 4 control points. You can simply apply the same translation and rotation to the control points and your equation would be translated/rotated.