orthogonal_rotation

rotates a point "orthogonally" around the origin

which I can't think of a good defintion for what I mean by "orthogonally". But right now the best way to describe it is to show how it affects a set of points

An array of points

(the position in the array represents its cartesian coordinates)

100 101 102 103 104 105 106 107 108
109 110 111 112 113 114 115 116 117
118 119 120 121 122 123 124 125 126
127 128 129 130 131 132 133 134 135
136 137 138 139 140 141 142 143 144
145 146 147 148 149 150 151 152 153
154 155 156 157 158 159 160 161 162
163 164 165 166 167 168 169 170 171
172 173 174 175 176 177 178 179 180

rotated with value 140 representing the center, with the value 0.25

it rotates the array 90 degrees counterclockwise

108 117 126 135 144 153 162 171 180
107 116 125 134 143 152 161 170 179
106 115 124 133 142 151 160 169 178
105 114 123 132 141 150 159 168 177
104 113 122 131 140 149 158 167 176
103 112 121 130 139 148 157 166 175
102 111 120 129 138 147 156 165 174
101 110 119 128 137 146 155 164 173
100 109 118 127 136 145 154 163 172

Or rotated with 140 as the center with the value 0.125

it rotates the array so the diagonals become the x and y axis lines of the axis clockwise of them (the list of points 100, 110, 120 that used to go through the top left to bottom right diagonal now go left to right)

104 105 106 107 108 117 126 135 144
103 113 114 115 116 125 134 143 153
102 112 122 123 124 133 142 152 162
101 111 121 131 132 141 151 161 171
100 110 120 130 140 150 160 170 180
109 119 129 139 148 149 159 169 179
118 128 138 147 156 157 158 168 178
127 137 146 155 164 165 166 167 177
136 145 154 163 172 173 174 175 176

Or at odder angles like 0.0287

which shifts each point 2 units clockwise while maintaining the same ( x + y instead of sqrt(x^2 + y^2) ) distance from the origin

102 103 104 105 106 107 108 117 126
101 111 112 113 114 115 116 125 135
100 110 121 122 123 124 133 134 144
109 119 120 130 131 132 142 143 153
118 128 129 139 140 141 151 152 162
127 137 138 148 149 150 160 161 171
136 146 147 156 157 158 159 170 180
145 155 164 165 166 167 168 169 179
154 163 172 173 174 175 176 177 178

I made this for my chess game so that each of the 64 squares can be rotated an amount

and each square if rotated the same amount, will be mapped to a square that none of the other squares are mapped to

and it does some things in a way that are useful for my game