I need help with a little equation solving problem
BlitzMax Forums/BlitzMax Programming/I need help with a little equation solving problem
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| As part of a little project that I am working on, I have the following math challenge to solve: I use the following two lines to convert 3D into screen space (simplified). xScreenCoord = (x-z) * Math.cos(0.46) yScreenCoord = (y+(x-z) * Math.sin(0.46) My challenge is to produce a solution that I can feed xScreenCoord, yScreenCoord and the 'y' component into to get 'x' and 'z' values. PS: Please don't suggest to use lookup tables. The app supports dimetric projections and a certain level of rotation around y. All the functions are based on the skeleton above and changing it would be a massive headache. Your help would be really appreciated. |
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| Rearrange the two equations: x-z = xScreenCoord/Math.cos(0.46) x-z = yScreenCoord/Math.sin(0.46) - y So it has to be the case that xScreenCoord/Math.cos(0.46) = yScreenCoord/Math.sin(0.46) - y = A for some value A. So we have x-z = A x-z = A which isn't enough to solve for x and z. So it isn't possible. You can pick an arbitrary value of x or z and work out the other one, but there isn't a unique solution. |
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| Thank Warpy. IRC #MATH on EFNET solved it :) x=(Math.cos(0.46)*(v-y)+Math.sin(0.46)*u)/(2*Math.cos(0.46)*Math.sin(0.46)) z=(Math.cos(0.46)*(v-y)-Math.sin(0.46)*u)/(2*Math.cos(0.46)*Math.sin(0.46)) u stands for xScreenCoord and v for yScreenCoord Last edited 2011 |
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| Ah, I misread the brackets! You're missing a right bracket on the second equation. |
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| Yes indeed, the second one isn't balanced and missing a closing bracket at the end. Here is the equation in action: http://www.isowerk.com/dev/v1/src/examples/test1.html It's a HTML5 test page that works anywhere except IE8 and below. |
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| That demo is freaking hot. |
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| Ah no, I was right the first time with what you'd written. You meant to put (x+z) in the second equation, not (x-z). |
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