Mercury Geometry and Math Library
| リビジョン | 433910f31212e2241658adbc8b8f5da607874987 (tree) |
|---|---|
| 日時 | 2022-01-24 09:26:24 |
| 作者 | AlaskanEmily <emily@alas...> |
| コミッター | AlaskanEmily |
Fix formatting in matrix.m
| @@ -6,16 +6,16 @@ | ||
| 6 | 6 | |
| 7 | 7 | :- module matrix. |
| 8 | 8 | |
| 9 | -%==============================================================================% | |
| 9 | +%=============================================================================% | |
| 10 | 10 | :- interface. |
| 11 | -%==============================================================================% | |
| 11 | +%=============================================================================% | |
| 12 | 12 | |
| 13 | 13 | :- use_module vector. |
| 14 | 14 | |
| 15 | 15 | :- include_module matrix.invert. |
| 16 | 16 | :- use_module matrix.invert. |
| 17 | 17 | |
| 18 | -%------------------------------------------------------------------------------% | |
| 18 | +%-----------------------------------------------------------------------------% | |
| 19 | 19 | |
| 20 | 20 | :- type matrix ---> matrix( |
| 21 | 21 | a::vector.vector4, |
| @@ -23,40 +23,40 @@ | ||
| 23 | 23 | c::vector.vector4, |
| 24 | 24 | d::vector.vector4). |
| 25 | 25 | |
| 26 | -%------------------------------------------------------------------------------% | |
| 26 | +%-----------------------------------------------------------------------------% | |
| 27 | 27 | % frustum(Left, Right, Top, Bottom, Near, Far) = Frustum. |
| 28 | 28 | :- func frustum(float, float, float, float, float, float) = matrix. |
| 29 | 29 | |
| 30 | -%------------------------------------------------------------------------------% | |
| 30 | +%-----------------------------------------------------------------------------% | |
| 31 | 31 | |
| 32 | 32 | :- func translate(float, float, float) = matrix. |
| 33 | 33 | |
| 34 | -%------------------------------------------------------------------------------% | |
| 34 | +%-----------------------------------------------------------------------------% | |
| 35 | 35 | |
| 36 | 36 | :- func translate(vector.vector3) = matrix. |
| 37 | 37 | |
| 38 | -%------------------------------------------------------------------------------% | |
| 38 | +%-----------------------------------------------------------------------------% | |
| 39 | 39 | |
| 40 | 40 | :- func scale(float, float, float) = matrix. |
| 41 | 41 | |
| 42 | -%------------------------------------------------------------------------------% | |
| 42 | +%-----------------------------------------------------------------------------% | |
| 43 | 43 | |
| 44 | 44 | :- func scale(vector.vector3) = matrix. |
| 45 | 45 | |
| 46 | -%------------------------------------------------------------------------------% | |
| 46 | +%-----------------------------------------------------------------------------% | |
| 47 | 47 | |
| 48 | 48 | :- func rotate(float::in, vector.vector3::in) = (matrix::uo) is det. |
| 49 | 49 | :- func rotate_old(float::in, vector.vector3::in) = (matrix::uo) is det. |
| 50 | 50 | |
| 51 | -%------------------------------------------------------------------------------% | |
| 51 | +%-----------------------------------------------------------------------------% | |
| 52 | 52 | |
| 53 | 53 | :- func identity = matrix. |
| 54 | 54 | |
| 55 | -%------------------------------------------------------------------------------% | |
| 55 | +%-----------------------------------------------------------------------------% | |
| 56 | 56 | |
| 57 | 57 | :- func transpose(matrix) = matrix. |
| 58 | 58 | |
| 59 | -%------------------------------------------------------------------------------% | |
| 59 | +%-----------------------------------------------------------------------------% | |
| 60 | 60 | |
| 61 | 61 | :- pred transpose(matrix, matrix). |
| 62 | 62 | :- mode transpose(in, out) is det. |
| @@ -67,15 +67,15 @@ | ||
| 67 | 67 | :- mode transpose(mdi, muo) is det. |
| 68 | 68 | :- mode transpose(muo, mdi) is det. |
| 69 | 69 | |
| 70 | -%------------------------------------------------------------------------------% | |
| 70 | +%-----------------------------------------------------------------------------% | |
| 71 | 71 | |
| 72 | 72 | :- func (matrix::in) * (vector.vector4::in) = (vector.vector4::uo) is det. |
| 73 | 73 | |
| 74 | -%------------------------------------------------------------------------------% | |
| 74 | +%-----------------------------------------------------------------------------% | |
| 75 | 75 | |
| 76 | 76 | :- func transform(matrix::in, vector.vector4::in) = (vector.vector4::uo) is det. |
| 77 | 77 | |
| 78 | -%------------------------------------------------------------------------------% | |
| 78 | +%-----------------------------------------------------------------------------% | |
| 79 | 79 | |
| 80 | 80 | :- func multiply(matrix, matrix) = matrix. |
| 81 | 81 | :- mode multiply(in, in) = (uo) is det. |
| @@ -97,18 +97,18 @@ | ||
| 97 | 97 | :- mode multiply2(in, di, uo) is det. |
| 98 | 98 | :- mode multiply2(di, di, uo) is det. |
| 99 | 99 | |
| 100 | -%------------------------------------------------------------------------------% | |
| 100 | +%-----------------------------------------------------------------------------% | |
| 101 | 101 | |
| 102 | 102 | :- func column_a(matrix::in) = (vector.vector4::uo) is det. |
| 103 | 103 | :- func column_b(matrix::in) = (vector.vector4::uo) is det. |
| 104 | 104 | :- func column_c(matrix::in) = (vector.vector4::uo) is det. |
| 105 | 105 | :- func column_d(matrix::in) = (vector.vector4::uo) is det. |
| 106 | 106 | |
| 107 | -%==============================================================================% | |
| 107 | +%=============================================================================% | |
| 108 | 108 | :- implementation. |
| 109 | -%==============================================================================% | |
| 109 | +%=============================================================================% | |
| 110 | 110 | |
| 111 | -:- import_module exception. | |
| 111 | +:- use_module exception. | |
| 112 | 112 | :- import_module float. |
| 113 | 113 | :- import_module int. |
| 114 | 114 | :- use_module math. |
| @@ -116,7 +116,7 @@ | ||
| 116 | 116 | :- import_module vector.vector3. |
| 117 | 117 | :- import_module vector.vector4. |
| 118 | 118 | |
| 119 | -%------------------------------------------------------------------------------% | |
| 119 | +%-----------------------------------------------------------------------------% | |
| 120 | 120 | |
| 121 | 121 | frustum(Left, Right, Top, Bottom, Near, Far) = matrix( |
| 122 | 122 | vector(2.0 * Near / (Right - Left), 0.0, A, 0.0), |
| @@ -128,7 +128,7 @@ frustum(Left, Right, Top, Bottom, Near, Far) = matrix( | ||
| 128 | 128 | C = -(Far + Near) / (Far - Near), |
| 129 | 129 | D = -2.0 * Far * Near / (Far - Near). |
| 130 | 130 | |
| 131 | -%------------------------------------------------------------------------------% | |
| 131 | +%-----------------------------------------------------------------------------% | |
| 132 | 132 | |
| 133 | 133 | translate(X, Y, Z) = matrix( |
| 134 | 134 | vector(1.0, 0.0, 0.0, X), |
| @@ -136,11 +136,11 @@ translate(X, Y, Z) = matrix( | ||
| 136 | 136 | vector(0.0, 0.0, 1.0, Z), |
| 137 | 137 | vector(0.0, 0.0, 0.0, 1.0)). |
| 138 | 138 | |
| 139 | -%------------------------------------------------------------------------------% | |
| 139 | +%-----------------------------------------------------------------------------% | |
| 140 | 140 | |
| 141 | 141 | translate(vector(X, Y, Z)) = translate(X, Y, Z). |
| 142 | 142 | |
| 143 | -%------------------------------------------------------------------------------% | |
| 143 | +%-----------------------------------------------------------------------------% | |
| 144 | 144 | |
| 145 | 145 | scale(X, Y, Z) = matrix( |
| 146 | 146 | vector(X, 0.0, 0.0, 0.0), |
| @@ -148,15 +148,15 @@ scale(X, Y, Z) = matrix( | ||
| 148 | 148 | vector(0.0, 0.0, Z, 0.0), |
| 149 | 149 | vector(0.0, 0.0, 0.0, 1.0)). |
| 150 | 150 | |
| 151 | -%------------------------------------------------------------------------------% | |
| 151 | +%-----------------------------------------------------------------------------% | |
| 152 | 152 | |
| 153 | 153 | scale(vector(X, Y, Z)) = scale(X, Y, Z). |
| 154 | 154 | |
| 155 | -%------------------------------------------------------------------------------% | |
| 155 | +%-----------------------------------------------------------------------------% | |
| 156 | 156 | |
| 157 | 157 | rotate_old(A, Vec) = M :- transpose(rotate(A, Vec), M). |
| 158 | 158 | |
| 159 | -%------------------------------------------------------------------------------% | |
| 159 | +%-----------------------------------------------------------------------------% | |
| 160 | 160 | |
| 161 | 161 | rotate(A, Vec) = matrix( |
| 162 | 162 | vector(X*X*(1.0-C)+C, X*Y*(1.0-C)-Z*S, X*Z*(1.0-C)+Y*S, 0.0), |
| @@ -167,7 +167,7 @@ rotate(A, Vec) = matrix( | ||
| 167 | 167 | S = math.sin(A), |
| 168 | 168 | C = math.cos(A). |
| 169 | 169 | |
| 170 | -%------------------------------------------------------------------------------% | |
| 170 | +%-----------------------------------------------------------------------------% | |
| 171 | 171 | |
| 172 | 172 | identity = matrix( |
| 173 | 173 | vector(1.0, 0.0, 0.0, 0.0), |
| @@ -175,20 +175,20 @@ identity = matrix( | ||
| 175 | 175 | vector(0.0, 0.0, 1.0, 0.0), |
| 176 | 176 | vector(0.0, 0.0, 0.0, 1.0)). |
| 177 | 177 | |
| 178 | -%------------------------------------------------------------------------------% | |
| 178 | +%-----------------------------------------------------------------------------% | |
| 179 | 179 | |
| 180 | 180 | (matrix(V1, V2, V3, V4)) * (V) = |
| 181 | 181 | vector(vector.dot(V, V1), vector.dot(V, V2), vector.dot(V, V3), vector.dot(V, V4)). |
| 182 | 182 | |
| 183 | -%------------------------------------------------------------------------------% | |
| 183 | +%-----------------------------------------------------------------------------% | |
| 184 | 184 | |
| 185 | 185 | transform(M, V) = (M * V). |
| 186 | 186 | |
| 187 | -%------------------------------------------------------------------------------% | |
| 187 | +%-----------------------------------------------------------------------------% | |
| 188 | 188 | |
| 189 | 189 | transpose(M1) = M2 :- transpose(M1, M2). |
| 190 | 190 | |
| 191 | -%------------------------------------------------------------------------------% | |
| 191 | +%-----------------------------------------------------------------------------% | |
| 192 | 192 | |
| 193 | 193 | transpose( |
| 194 | 194 | matrix( |
| @@ -202,7 +202,7 @@ transpose( | ||
| 202 | 202 | vector(C, G, K, O), |
| 203 | 203 | vector(D, H, L, P))). |
| 204 | 204 | |
| 205 | -%------------------------------------------------------------------------------% | |
| 205 | +%-----------------------------------------------------------------------------% | |
| 206 | 206 | |
| 207 | 207 | multiply(matrix(A, B, C, D), matrix(AIn, BIn, CIn, DIn)) = matrix( |
| 208 | 208 | vector(vector.dot(A, E), vector.dot(A, F), vector.dot(A, G), vector.dot(A, H)), |
| @@ -218,9 +218,10 @@ multiply(M1, M2, multiply(M1, M2)). | ||
| 218 | 218 | |
| 219 | 219 | multiply2(M2, M1, multiply(M1, M2)). |
| 220 | 220 | |
| 221 | -%------------------------------------------------------------------------------% | |
| 221 | +%-----------------------------------------------------------------------------% | |
| 222 | 222 | |
| 223 | 223 | column_a(M) = vector(M ^ a ^ x + 0.0, M ^ b ^ x + 0.0, M ^ c ^ x + 0.0, M ^ d ^ x + 0.0). |
| 224 | 224 | column_b(M) = vector(M ^ a ^ y + 0.0, M ^ b ^ y + 0.0, M ^ c ^ y + 0.0, M ^ d ^ y + 0.0). |
| 225 | 225 | column_c(M) = vector(M ^ a ^ z + 0.0, M ^ b ^ z + 0.0, M ^ c ^ z + 0.0, M ^ d ^ z + 0.0). |
| 226 | 226 | column_d(M) = vector(M ^ a ^ w + 0.0, M ^ b ^ w + 0.0, M ^ c ^ w + 0.0, M ^ d ^ w + 0.0). |
| 227 | + |
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matrix.m