Math meets art.
Printed From: Pixel Joint
Category: The Lounge
Forum Name: Resources and Support
Forum Discription: Help your fellow pixel artists out with links to good tutorials, other forums, software, fonts, etc. Bugs and support issues should go here as well.
URL: https://pixeljoint.com/forum/forum_posts.asp?TID=3222
Printed Date: 13 September 2025 at 3:00pm
Topic: Math meets art.
Posted By: Pixel_Outlaw
Subject: Math meets art.
Date Posted: 17 October 2006 at 9:03pm
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OK I plan to list some usefull math to help make pixel art.
-Play along it's more text than trouble.-
This formula will find a point a given distance and direction away from a base point.
startx= the starting pointx
starty= the starting pointy
radius= the distance away you want the new point
ok now we have to fid the new points x and y
endx=basex+cos(angle)*radius
endy=basey+sin(angle)*radius
Why would you use this you ask? Well lets say you have objects you want arranged in a circle around a central point, now you simply incriment the angles and use the same starting point and you have evenly spaced objects.
Also you can use this to make PERFECT iso circles you simply use the radius/2 for the y radius.
Lets try it out and see how it works.
Ok we have a pixel ar (12,3) and we want to put a planet at a 45 degree angle away from it with a radius of 24 pixels.
Ok we know our base point x and y
basex=12
basey=3
radius=24
angle= 45
endx=basex+cos(angle)*radius - this will find the new x coordinate
endy=basey+sin(angle)*radius - this will find the new y coordinate
endx=12+cos(45)*24 = 28.97 rounded to 29 *note never truncate
endy=3+sin(45)*24 = 19.97 rounded to 20
Hope it helps! I'll have more soon.
this could be used to make perfect triangles and other ngons by using more than one angle.
Lets say we want to make a perfect triangle.
We would use the angles 0,120,240 and our base point would reside in the middle. If we want to rotate the direction of the triangle we simply add the same rotation angle to all of the angles. If you want to rotate your triangle 10 degrees the angles for the formula would be (10,130,250).
You use the same base point for basex and basey, you only change the angle variable. If you are willing to spend the time you can get breat results.
It gets a bit more diffcult when you are working with even widths as they have no central point, you have to use the four points that form the middle "cluster".
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Replies:
Posted By: jalonso
Date Posted: 17 October 2006 at 9:51pm
It needs some AA and maybe some dithering too 
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Posted By: Blueberry_pie
Date Posted: 18 October 2006 at 3:35am
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I am confused by the lack of pretty pictures!
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Posted By: Pixel_Outlaw
Date Posted: 18 October 2006 at 6:39am
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sorry guys I have to go to school, I'll add more this afternoon. ------------- http://www.shmup-dev.com/forum/">
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Posted By: Pixel_Outlaw
Date Posted: 18 October 2006 at 2:13pm
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Ok this is a TRUE iso cube made with 6 angle calculations and one centerpoit. The radius is 32 pixels.
http://imageshack.us">  If you wanted to make it point up you would just take the angles shown here and add 15 degrees to each angle. This is not the main point for this though. These cubes don't tesselate well this is just a demo. Just to give you an idea of what you can do. I used the radius of 32 and the angles of a hexagon to find the points, then I simply connected them. Really you could do professionaly made 3D art if you have the time you can make any polygon or any polyhedron.------------- http://www.shmup-dev.com/forum/">
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Posted By: Pixel_Outlaw
Date Posted: 18 October 2006 at 2:22pm
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Originally posted by Pixel_Outlaw
Ok this is a TRUE iso cube made with 6 angle calculations and one centerpoit. The radius is 32 pixels. http://imageshack.us"> If you wanted to make it point up you would just take the angles shown here and add 15 degrees to each angle. This is not the main point for this though. These cubes don't tesselate well this is just a demo. Just to give you an idea of what you can do. I used the radius of 32 and the angles of a hexagon to find the points, then I simply connected them. Really you could do professionaly made 3D art if you have the time you can make any polygon or any polyhedron.There are many uses for this. Ok you want your wheel to be divided into equal sections for spokes? Simply decide how many spokes you want then use 360/num_angles to get the incriment value for each spoke. ------------- http://www.shmup-dev.com/forum/">
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