{"id":18,"date":"2019-09-25T22:23:15","date_gmt":"2019-09-25T20:23:15","guid":{"rendered":"http:\/\/douglashalse.com\/?p=18"},"modified":"2019-10-13T22:51:04","modified_gmt":"2019-10-13T20:51:04","slug":"spherical-coordinates","status":"publish","type":"post","link":"https:\/\/douglashalse.com\/index.php\/2019\/09\/25\/spherical-coordinates\/","title":{"rendered":"Spherical Coordinates for a Third-person perspective"},"content":{"rendered":"\n

The Idea<\/h2>\n\n\n\n

I have always been fond of the Third person perspective in video games and after my course about multivariate analysis, I finally understood how I can pull it off.<\/p>\n\n\n\n

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A video game typically uses Cartesian coordinates (X Y Z) for the game logic but in order to have a rotating camera around the player, I implemented a Coordinate system conversion in order to interface with the coordinates of the game. The Cartesian coordinates are converted to Spherical coordinates with the variables now being:<\/p>\n\n\n\n

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One thing to keep in mind is that formula for phi does not return the desired angle, for example, x<0. A modified version of Acrtan called Arctan2 is used that always returns the angle for any given x and y.<\/p>\n<\/div>\n\n\n\n

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A Third person perspective for a character<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n

The Code<\/h2>\n\n\n\n
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I decided to use the Game engine Unity to make the camera and I started with creating a blank scene and put a plane to represent the ground and a capsule to represent the player. <\/p>\n\n\n\n

I created a script called cameraController and made sure that I could link the camera and the capsule to the script to get information like its world position. If you want to you can read the code here<\/a>.<\/p>\n<\/div>\n\n\n\n

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The lonely player in the vast open void.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n

I also made a Character controller to move the capsule but it had to move in the expected direction as seen from the camera so with some simple vector mathematics I defined the controller here<\/a>. <\/p>\n\n\n\n

Notice how I determine the desired direction for the buttons A and D with a cross product of the projected vector from the camera to the capsule onto the xz-plane and a vector normal to that plane. This returns the vector orthogonal to those two vectors and is the direction I want the capsule to travel in.<\/p>\n\n\n\n

The Demo<\/h2>\n\n\n\n

Here is a demo of the code running. I did add some slight movement interpolation to smooth out the animation of both the camera movement and the rotation of the camera to make it more presentable.<\/p>\n\n\n\n

I made a little course that I used to test the movement and camera controls. <\/p>\n\n\n\n