Details | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 4 | daniel-mar | 1 | unit D3DUtils; |
| 2 | |||
| 3 | interface |
||
| 4 | |||
| 5 | {$INCLUDE DelphiXcfg.inc} |
||
| 6 | |||
| 7 | uses |
||
| 8 | Windows, Math, |
||
| 9 | {$IFDEF StandardDX} |
||
| 10 | {$IFDEF VER14UP} DXTypes, {$ENDIF} Direct3D, DirectDraw; |
||
| 11 | {$ELSE} |
||
| 12 | DirectX; |
||
| 13 | {$ENDIF} |
||
| 14 | |||
| 15 | const |
||
| 16 | g_PI = 3.14159265358979323846; // Pi |
||
| 17 | g_Uhel = g_PI / 180; |
||
| 18 | g_2_PI = 6.28318530717958623200; // 2 * Pi |
||
| 19 | g_PI_DIV_2 = 1.57079632679489655800; // Pi / 2 |
||
| 20 | g_PI_DIV_4 = 0.78539816339744827900; // Pi / 4 |
||
| 21 | g_INV_PI = 0.31830988618379069122; // 1 / Pi |
||
| 22 | g_DEGTORAD = 0.01745329251994329547; // Degrees to Radians |
||
| 23 | g_RADTODEG = 57.29577951308232286465; // Radians to Degrees |
||
| 24 | g_HUGE = 1.0E+38; // Huge number for FLOAT |
||
| 25 | g_EPSILON = 1.0E-5; // Tolerance for FLOATs |
||
| 26 | |||
| 27 | type |
||
| 28 | TD2DVector = packed record |
||
| 29 | X, Y: Single; |
||
| 30 | end; |
||
| 31 | TD3DHVector = packed record |
||
| 32 | X, Y, Z, W: Single; |
||
| 33 | end; |
||
| 34 | TQuaternion = packed record |
||
| 35 | case Integer of |
||
| 36 | 0: (X, Y, Z, W: Single); //like TD3DHVector |
||
| 37 | 1: ( |
||
| 38 | V: TD3DVector; |
||
| 39 | ); |
||
| 40 | end; |
||
| 41 | function ProjectionMatrix(near_plane, far_plane, fov_horiz, fov_vert: real): TD3DMatrix; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 42 | //-------------------------- |
||
| 43 | // 3D Vector |
||
| 44 | //-------------------------- |
||
| 45 | function MakeD3DVector(x, y, z: TD3DValue): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 46 | function MakeD2DVector(x, y: TD3DValue): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 47 | function MakeD3DVertex(hv, nv: TD3DVector; tu, tv: TD3DValue): TD3DVertex; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 48 | function MakeD3DVertex(hx, hy, hz, nx, ny, nz, tu, tv: TD3DValue): TD3DVertex; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 49 | function MakeD3DLVertex(hv: TD3DVector; col, sp: DWORD; tu, tv: TD3DValue): TD3DLVertex; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 50 | function MakeD3DLVertex(hx, hy, hz: TD3DValue; col, sp: DWORD; tu, tv: TD3DValue): TD3DLVertex; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 51 | function MakeD3DTLVertex(hx, hy, hz, rhw: TD3DValue; col, sp: DWORD; tu, tv: TD3DValue): TD3DTLVERTEX; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 52 | function MakeD3DTLVertex(hv: TD3DVector; rhw: TD3DValue; col, sp: DWORD; tu, tv: TD3DValue): TD3DTLVERTEX; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 53 | function Vector2RGBA(const v: TD3DVector; fHeight: Single): DWord; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 54 | function VectorToRGB(NormalVector: TD3DVector): DWORD; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 55 | //-------------------------- |
||
| 56 | // 3D Vector |
||
| 57 | //-------------------------- |
||
| 58 | function Quaternion(_w, _x, _y, _z: Single): TQuaternion; |
||
| 59 | function QuaternionLength(const a: TQuaternion): Single; |
||
| 60 | function QuaternionNormalize(const a: TQuaternion): TQuaternion; |
||
| 61 | |||
| 62 | function D3DMath_VecNormalize(const v: TD3DVector): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 63 | function D3DMath_VecViewScreenize(const v: TD3DHVector): TD3DHVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 64 | function D3DMath_VecHeterogenize(const hv: TD3DHVector; _div: Boolean{$IFDEF VER4UP} = False{$ENDIF}): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 65 | function D3DMath_VecHomogenize(const v: TD3DVector): TD3DHVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 66 | function D3DMath_VecTransform(const a: TD3DHVector; const m: TD3DMATRIX): TD3DHVector; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 67 | function D3DMath_VecTransform(const a: TD3DVector; const m: TD3DMATRIX): TD3DVector; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 68 | function D3DMath_Vec3Length(const v: TD3DVector): TD3DValue; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 69 | function D3DMath_Vec3LengthSq(const v: TD3DVector): TD3DValue; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 70 | function D3DMath_Vec3Dot(const v1, v2: TD3DVector): TD3DValue; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 71 | function D3DMath_Vec3Cross(const v1, v2: TD3DVector): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 72 | function D3DMath_Vec3Add(const v1, v2: TD3DVector): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 73 | function D3DMath_Vec3Subtract(const v1, v2: TD3DVector): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 74 | function D3DMath_Vec3Minimize(const v1, v2: TD3DVector): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 75 | function D3DMath_Vec3Maximize(const v1, v2: TD3DVector): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 76 | function D3DMath_Vec3Scale(const v: TD3DVector; const s: TD3DValue): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 77 | function D3DMath_Vec3Lerp(out vOut: TD3DVector; const v1, v2: TD3DVector; const s: TD3DValue): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 78 | |||
| 79 | function D3DMath_IsZero(a: Double; fTol: Double { = g_EPSILON}): Boolean; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 80 | |||
| 81 | procedure D3DMath_QuaternionFromRotation(var x, y, z, w: Double; const v: TD3DVector; fTheta: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 82 | function D3DMath_QuaternionFromRotation(const axis: TD3DVector; const r: Double): TQuaternion; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 83 | procedure D3DMath_RotationFromQuaternion(var v: TD3DVector; var fTheta: Double; x, y, z, w: Double); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 84 | procedure D3DMath_QuaternionFromAngles(var x, y, z, w: Double; fYaw, fPitch, fRoll: Double); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 85 | procedure D3DMath_MatrixFromQuaternion(var mat: TD3DMatrix; x, y, z, w: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 86 | function D3DMath_MatrixFromQuaternion(q: TQuaternion): TD3DMatrix; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 87 | procedure D3DMath_QuaternionFromMatrix(var x, y, z, w: Double; var mat: TD3DMatrix); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 88 | procedure D3DMath_QuaternionMultiply(var Qx, Qy, Qz, Qw: Double; Ax, Ay, Az, Aw, Bx, By, Bz, Bw: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 89 | function D3DMath_QuaternionMultiply(a, b: TQuaternion): TQuaternion; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 90 | procedure D3DMath_QuaternionSlerp(var Qx, Qy, Qz, Qw: Double; Ax, Ay, Az, Aw, Bx, By, Bz, Bw, fAlpha: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 91 | function D3DMath_QuaternionSlerp(A, B: TQuaternion; fAlpha: Double): TQuaternion; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 92 | |||
| 93 | procedure D3DUtil_InitSurfaceDesc(var ddsd: TDDSurfaceDesc2; dwFlags, dwCaps: DWORD); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 94 | procedure D3DUtil_InitMaterial(var mtrl: TD3DMaterial7; r, g, b, a: Double); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 95 | procedure D3DUtil_InitLight(var light: TD3DLight7; ltType: TD3DLightType; x, y, z: Double); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 96 | |||
| 97 | procedure D3DMath_MatrixMultiply(var q: TD3DMatrix; const a, b: TD3DMatrix); overload; |
||
| 98 | function D3DMath_MatrixMultiply(const a, b: TD3DMatrix): TD3DMatrix; overload; |
||
| 99 | function D3DMath_MatrixInvert(var q: TD3DMatrix; const a: TD3DMatrix): HResult; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 100 | function D3DMath_MatrixInvert(const a: TD3DMatrix): TD3DMatrix; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 101 | function D3DMath_VectorMatrixMultiply(var vDest: TD3DVector; const vSrc: TD3DVector; const mat: TD3DMatrix): HResult; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 102 | function D3DMath_VertexMatrixMultiply(var vDest: TD3DVertex; const vSrc: TD3DVertex; const mat: TD3DMatrix): HResult; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 103 | procedure D3DUtil_SetIdentityMatrix(out m: TD3DMatrix); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 104 | function D3DUtil_SetIdentityMatrix: TD3DMatrix; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 105 | function D3DUtil_SetScaleMatrix(const x, y, z: Single): TD3DMatrix; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 106 | function D3DUtil_SetViewMatrix(var mat: TD3DMatrix; const vFrom, vAt, vWorldUp: TD3DVector): HResult; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 107 | function D3DUtil_SetProjectionMatrix(var mat: TD3DMatrix; fFOV, fAspect, fNearPlane, fFarPlane: Double): HResult; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 108 | procedure D3DUtil_SetRotateXMatrix(var mat: TD3DMatrix; fRads: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 109 | function D3DUtil_SetRotateXMatrix(fRads: Double): TD3DMatrix; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 110 | procedure D3DUtil_SetRotateYMatrix(var mat: TD3DMatrix; fRads: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 111 | function D3DUtil_SetRotateYMatrix(fRads: Double): TD3DMatrix; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 112 | procedure D3DUtil_SetRotateZMatrix(var mat: TD3DMatrix; fRads: Double); overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 113 | function D3DUtil_SetRotateZMatrix(fRads: Double): TD3DMatrix; overload; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 114 | procedure D3DUtil_SetRotationMatrix(var mat: TD3DMatrix; var vDir: TD3DVector; fRads: Double); {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 115 | function D3DUtil_SetRotationMatrixByX(const a: TD3DVector; const r: Double): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 116 | function D3DUtil_SetRotationMatrixByY(const a: TD3DVector; const r: Double): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 117 | function D3DUtil_SetRotationMatrixByZ(const a: TD3DVector; const r: Double): TD3DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 118 | |||
| 119 | function D3DCOLOR_ARGB(a, r, g, b: Cardinal): TD3DColor; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 120 | function D3DCOLOR_RGBA(r, g, b, a: Cardinal): TD3DColor; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 121 | function D3DCOLOR_XRGB(r, g, b: Cardinal): TD3DColor; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 122 | function D3DCOLOR_COLORVALUE(r, g, b, a: Single): TD3DColor; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 123 | |||
| 124 | // simple D2D operation |
||
| 125 | |||
| 126 | function D2DMath_VecAdd(const a: TD2DVector; const b: TD2DVector): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 127 | function D2DMath_VecSub(const a: TD2DVector; const b: TD2DVector): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 128 | function D2DMath_VecDotProduct(const a, b: TD2DVector): Single; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 129 | function D2DMath_VecDistance(const a, b: TD2DVector): Single; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 130 | function D2DMath_VecLength(const a: TD2DVector): Single; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 131 | function D2DMath_VecNormalize(const a: TD2DVector): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 132 | function D2DMath_VecToAngle(const a: TD2DVector): Double; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 133 | function D2DMath_VecRot(const a: TD2DVector; const angle: Double): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 134 | function D2DMath_VecScale(const a: TD2DVector; const scale: Double): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 135 | function D2DMath_VecChangeLength(const a: TD2DVector; const k: Single): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 136 | function D2DMath_VecLookAt(const pos: TD2DVector; const target: TD2DVector; const k: Single): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 137 | function D2DMath_VecRandom2D(const k: Single): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 138 | |||
| 139 | function D2DMath_VecLerp(const a: TD2DVector; const b: TD2DVector; const rate: Single): TD2DVector; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 140 | |||
| 141 | implementation |
||
| 142 | |||
| 143 | //function RSin(val: Integer): Double; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 144 | //begin |
||
| 145 | // Result := Sin(val / 2048.0 * Pi); |
||
| 146 | //end; |
||
| 147 | // |
||
| 148 | //function RCos(val: Integer): Double; {$IFDEF VER9UP}inline; {$ENDIF} |
||
| 149 | //begin |
||
| 150 | // Result := Cos(val / 2048.0 * Pi); |
||
| 151 | //end; |
||
| 152 | |||
| 153 | function Quaternion(_w, _x, _y, _z: Single): TQuaternion; |
||
| 154 | begin |
||
| 155 | Result.W := _w; |
||
| 156 | Result.X := _x; |
||
| 157 | Result.Y := _y; |
||
| 158 | Result.Z := _z; |
||
| 159 | end; |
||
| 160 | |||
| 161 | function QuaternionLength(const a: TQuaternion): Single; |
||
| 162 | begin |
||
| 163 | Result := Sqrt(a.w * a.w + a.x * a.x + a.y * a.y + a.z * a.z); |
||
| 164 | end; |
||
| 165 | |||
| 166 | function QuaternionNormalize(const a: TQuaternion): TQuaternion; |
||
| 167 | var |
||
| 168 | len: Single; |
||
| 169 | begin |
||
| 170 | len := QuaternionLength(a); |
||
| 171 | if len = 0.0 then |
||
| 172 | begin |
||
| 173 | Result := Quaternion(1, 0, 0, 0); |
||
| 174 | Exit; |
||
| 175 | end; |
||
| 176 | Result.x := a.X / len; |
||
| 177 | Result.y := a.Y / len; |
||
| 178 | Result.z := a.Z / len; |
||
| 179 | Result.w := a.W / len; |
||
| 180 | end; |
||
| 181 | |||
| 182 | function GetMatrixFromQuaternion(const a: TQuaternion): TD3DMatrix; |
||
| 183 | begin |
||
| 184 | |||
| 185 | end; |
||
| 186 | |||
| 187 | |||
| 188 | function D3DCOLOR_ARGB(a, r, g, b: Cardinal): TD3DColor; |
||
| 189 | begin |
||
| 190 | Result := (a shl 24) or (r shl 16) or (g shl 8) or b; |
||
| 191 | end; |
||
| 192 | |||
| 193 | function D3DCOLOR_RGBA(r, g, b, a: Cardinal): TD3DColor; |
||
| 194 | begin |
||
| 195 | Result := D3DCOLOR_ARGB(a, r, g, b); |
||
| 196 | end; |
||
| 197 | |||
| 198 | function D3DCOLOR_XRGB(r, g, b: Cardinal): TD3DColor; |
||
| 199 | begin |
||
| 200 | Result := D3DCOLOR_ARGB($FF, r, g, b); |
||
| 201 | end; |
||
| 202 | |||
| 203 | function D3DCOLOR_COLORVALUE(r, g, b, a: Single): TD3DColor; |
||
| 204 | begin |
||
| 205 | Result := D3DCOLOR_RGBA(Byte(Round(r * 255)), Byte(Round(g * 255)), Byte(Round(b * 255)), Byte(Round(a * 255))) |
||
| 206 | end; |
||
| 207 | |||
| 208 | function MakeD3DVector(x, y, z: TD3DValue): TD3DVector; |
||
| 209 | begin |
||
| 210 | Result.x := x; |
||
| 211 | Result.y := y; |
||
| 212 | Result.z := z; |
||
| 213 | end; |
||
| 214 | |||
| 215 | function MakeD2DVector(x, y: TD3DValue): TD2DVector; |
||
| 216 | begin |
||
| 217 | Result.x := x; |
||
| 218 | Result.y := y; |
||
| 219 | end; |
||
| 220 | |||
| 221 | function MakeD3DVertex(hv, nv: TD3DVector; tu, tv: TD3DValue): TD3DVertex; |
||
| 222 | begin |
||
| 223 | Result.x := hv.x; |
||
| 224 | Result.y := hv.y; |
||
| 225 | Result.z := hv.z; |
||
| 226 | Result.nx := nv.x; |
||
| 227 | Result.ny := nv.y; |
||
| 228 | Result.nz := nv.z; |
||
| 229 | Result.tu := tu; |
||
| 230 | Result.tv := tv; |
||
| 231 | end; |
||
| 232 | |||
| 233 | function MakeD3DVertex(hx, hy, hz, nx, ny, nz, tu, tv: TD3DValue): TD3DVertex; |
||
| 234 | begin |
||
| 235 | Result.x := hx; |
||
| 236 | Result.y := hy; |
||
| 237 | Result.z := hz; |
||
| 238 | Result.nx := nx; |
||
| 239 | Result.ny := ny; |
||
| 240 | Result.nz := nz; |
||
| 241 | Result.tu := tu; |
||
| 242 | Result.tv := tv; |
||
| 243 | end; |
||
| 244 | |||
| 245 | function MakeD3DLVertex(hv: TD3DVector; col, sp: DWORD; tu, tv: TD3DValue): TD3DLVertex; |
||
| 246 | begin |
||
| 247 | FillChar(Result, SizeOf(Result), 0); |
||
| 248 | Result.x := hv.x; |
||
| 249 | Result.y := hv.y; |
||
| 250 | Result.z := hv.z; |
||
| 251 | Result.color := col; |
||
| 252 | Result.specular := sp; |
||
| 253 | Result.tu := tu; |
||
| 254 | Result.tv := tv; |
||
| 255 | end; |
||
| 256 | |||
| 257 | function MakeD3DLVertex(hx, hy, hz: TD3DValue; col, sp: DWORD; tu, tv: TD3DValue): TD3DLVertex; |
||
| 258 | begin |
||
| 259 | FillChar(Result, SizeOf(Result), 0); |
||
| 260 | Result.x := hx; |
||
| 261 | Result.y := hy; |
||
| 262 | Result.z := hz; |
||
| 263 | Result.color := col; |
||
| 264 | Result.specular := sp; |
||
| 265 | Result.tu := tu; |
||
| 266 | Result.tv := tv; |
||
| 267 | end; |
||
| 268 | |||
| 269 | function MakeD3DTLVertex(hx, hy, hz, rhw: TD3DValue; col, sp: DWORD; tu, tv: TD3DValue): TD3DTLVERTEX; |
||
| 270 | begin |
||
| 271 | Result.sx := hx; |
||
| 272 | Result.sy := hy; |
||
| 273 | Result.sz := hz; |
||
| 274 | Result.dvRHW := rhw; |
||
| 275 | Result.color := col; |
||
| 276 | Result.specular := sp; |
||
| 277 | Result.tu := tu; |
||
| 278 | Result.tv := tv; |
||
| 279 | end; |
||
| 280 | |||
| 281 | function MakeD3DTLVertex(hv: TD3DVector; rhw: TD3DValue; col, sp: DWORD; tu, tv: TD3DValue): TD3DTLVERTEX; |
||
| 282 | begin |
||
| 283 | Result.sx := hv.x; |
||
| 284 | Result.sy := hv.y; |
||
| 285 | Result.sz := hv.z; |
||
| 286 | Result.dvRHW := rhw; |
||
| 287 | Result.color := col; |
||
| 288 | Result.specular := sp; |
||
| 289 | Result.tu := tu; |
||
| 290 | Result.tv := tv; |
||
| 291 | end; |
||
| 292 | |||
| 293 | function Vector2RGBA(const v: TD3DVector; fHeight: Single): DWord; |
||
| 294 | var |
||
| 295 | r, g, b, a: DWord; |
||
| 296 | begin |
||
| 297 | r := Round(127.0 * v.x + 128.0); |
||
| 298 | g := Round(127.0 * v.y + 128.0); |
||
| 299 | b := Round(127.0 * v.z + 128.0); |
||
| 300 | a := Round(255.0 * fHeight); |
||
| 301 | Result := ((a shl 24) + (r shl 16) + (g shl 8) + (b shl 0)); |
||
| 302 | end; |
||
| 303 | |||
| 304 | function VectorToRGB(NormalVector: TD3DVector): DWORD; |
||
| 305 | var dwR, dwG, dwB: DWORD; |
||
| 306 | begin |
||
| 307 | dwR := Round(127 * NormalVector.x + 128); |
||
| 308 | dwG := Round(127 * NormalVector.y + 128); |
||
| 309 | dwB := Round(127 * NormalVector.z + 128); |
||
| 310 | Result := $FF000000 + dwR shl 16 + dwG shl 8 + dwB; |
||
| 311 | end; |
||
| 312 | |||
| 313 | function ProjectionMatrix(near_plane, // distance to near clipping plane |
||
| 314 | far_plane, // distance to far clipping plane |
||
| 315 | fov_horiz, // horizontal field of view angle, in radians |
||
| 316 | fov_vert: real): TD3DMatrix; // vertical field of view angle, in radians |
||
| 317 | var h, w, Q: real; |
||
| 318 | begin |
||
| 319 | Fov_horiz := g_Uhel * Fov_horiz; |
||
| 320 | Fov_Vert := g_Uhel * Fov_Vert; |
||
| 321 | |||
| 322 | w := cotan(fov_horiz * 0.5); |
||
| 323 | h := cotan(fov_vert * 0.5); |
||
| 324 | Q := far_plane / (far_plane - near_plane); |
||
| 325 | |||
| 326 | result._11 := w; |
||
| 327 | result._22 := h; |
||
| 328 | result._33 := Q; |
||
| 329 | result._43 := -Q * near_plane; |
||
| 330 | result._34 := 1; |
||
| 331 | end; |
||
| 332 | // end of ProjectionMatrix() |
||
| 333 | |||
| 334 | //-------------------------- |
||
| 335 | // 3D Vector |
||
| 336 | //-------------------------- |
||
| 337 | |||
| 338 | function D3DMath_VecNormalize(const v: TD3DVector): TD3DVector; |
||
| 339 | var |
||
| 340 | len: Single; |
||
| 341 | begin |
||
| 342 | len := D3DMath_Vec3Length(v); |
||
| 343 | if len = 0 then |
||
| 344 | FillChar(Result, SizeOf(Result), 0) |
||
| 345 | else |
||
| 346 | begin |
||
| 347 | Result.X := v.X / len; |
||
| 348 | Result.Y := v.Y / len; |
||
| 349 | Result.Z := v.Z / len; |
||
| 350 | end; |
||
| 351 | end; |
||
| 352 | |||
| 353 | function D3DMath_VecViewScreenize(const v: TD3DHVector): TD3DHVector; |
||
| 354 | begin |
||
| 355 | with Result do |
||
| 356 | begin |
||
| 357 | if v.W <> 0.0 then |
||
| 358 | begin |
||
| 359 | W := 1.0 / v.W; |
||
| 360 | X := v.X * W; |
||
| 361 | Y := v.Y * W; |
||
| 362 | Z := v.Z * W; |
||
| 363 | end; |
||
| 364 | end; |
||
| 365 | end; |
||
| 366 | |||
| 367 | function D3DMath_VecHeterogenize(const hv: TD3DHVector; _div: Boolean): TD3DVector; |
||
| 368 | var |
||
| 369 | d: Single; |
||
| 370 | begin |
||
| 371 | if not _div then |
||
| 372 | begin |
||
| 373 | Result.x := hv.X; |
||
| 374 | Result.y := hv.Y; |
||
| 375 | Result.z := hv.Z; |
||
| 376 | end |
||
| 377 | else |
||
| 378 | begin |
||
| 379 | d := 1.0 / hv.w; |
||
| 380 | Result.x := hv.x * d; |
||
| 381 | Result.y := hv.y * d; |
||
| 382 | Result.z := hv.z * d; |
||
| 383 | end; |
||
| 384 | end; |
||
| 385 | |||
| 386 | function D3DMath_VecHomogenize(const v: TD3DVector): TD3DHVector; |
||
| 387 | begin |
||
| 388 | Move(v, result, Sizeof(TD3DVector)); |
||
| 389 | result.W := 1.0; |
||
| 390 | end; |
||
| 391 | |||
| 392 | function D3DMath_VecTransform(const a: TD3DHVector; const m: TD3DMATRIX): TD3DHVector; |
||
| 393 | begin |
||
| 394 | result.X := a.X * m._11 + a.Y * m._21 + a.Z * m._31 + a.W * m._41; |
||
| 395 | result.Y := a.X * m._12 + a.Y * m._22 + a.Z * m._32 + a.W * m._42; |
||
| 396 | result.Z := a.X * m._13 + a.Y * m._23 + a.Z * m._33 + a.W * m._43; |
||
| 397 | result.W := a.X * m._14 + a.Y * m._24 + a.Z * m._34 + a.W * m._44; |
||
| 398 | end; |
||
| 399 | |||
| 400 | function D3DMath_VecTransform(const a: TD3DVector; const m: TD3DMATRIX): TD3DVector; |
||
| 401 | begin |
||
| 402 | result.X := a.X * m._11 + a.Y * m._21 + a.Z * m._31 + m._41; |
||
| 403 | result.Y := a.X * m._12 + a.Y * m._22 + a.Z * m._32 + m._42; |
||
| 404 | result.Z := a.X * m._13 + a.Y * m._23 + a.Z * m._33 + m._43; |
||
| 405 | end; |
||
| 406 | |||
| 407 | function D3DMath_Vec3Length(const v: TD3DVector): TD3DValue; |
||
| 408 | begin |
||
| 409 | with v do Result := Sqrt(Sqr(x) + Sqr(y) + Sqr(z)); |
||
| 410 | end; |
||
| 411 | |||
| 412 | function D3DMath_Vec3LengthSq(const v: TD3DVector): TD3DValue; |
||
| 413 | begin |
||
| 414 | with v do Result := Sqr(x) + Sqr(y) + Sqr(z); |
||
| 415 | end; |
||
| 416 | |||
| 417 | function D3DMath_Vec3Dot(const v1, v2: TD3DVector): TD3DValue; |
||
| 418 | begin |
||
| 419 | Result := v1.x * v2.x + v1.y * v2.y + v1.z * v2.z; |
||
| 420 | end; |
||
| 421 | |||
| 422 | function D3DMath_Vec3Cross(const v1, v2: TD3DVector): TD3DVector; |
||
| 423 | begin |
||
| 424 | Result.x := v1.y * v2.z - v1.z * v2.y; |
||
| 425 | Result.y := v1.z * v2.x - v1.x * v2.z; |
||
| 426 | Result.z := v1.x * v2.y - v1.y * v2.x; |
||
| 427 | end; |
||
| 428 | |||
| 429 | function D3DMath_Vec3Add(const v1, v2: TD3DVector): TD3DVector; |
||
| 430 | begin |
||
| 431 | Result.x := v1.x + v2.x; |
||
| 432 | Result.y := v1.y + v2.y; |
||
| 433 | Result.z := v1.z + v2.z; |
||
| 434 | end; |
||
| 435 | |||
| 436 | function D3DMath_Vec3Subtract(const v1, v2: TD3DVector): TD3DVector; |
||
| 437 | begin |
||
| 438 | Result.x := v1.x - v2.x; |
||
| 439 | Result.y := v1.y - v2.y; |
||
| 440 | Result.z := v1.z - v2.z; |
||
| 441 | end; |
||
| 442 | |||
| 443 | // Minimize each component. x = min(x1, x2), y = min(y1, y2) |
||
| 444 | |||
| 445 | function D3DMath_Vec3Minimize(const v1, v2: TD3DVector): TD3DVector; |
||
| 446 | begin |
||
| 447 | if v1.x < v2.x then Result.x := v1.x else Result.x := v2.x; |
||
| 448 | if v1.y < v2.y then Result.y := v1.y else Result.y := v2.y; |
||
| 449 | if v1.z < v2.z then Result.z := v1.z else Result.z := v2.z; |
||
| 450 | end; |
||
| 451 | |||
| 452 | // Maximize each component. x = max(x1, x2), y = max(y1, y2) |
||
| 453 | |||
| 454 | function D3DMath_Vec3Maximize(const v1, v2: TD3DVector): TD3DVector; |
||
| 455 | begin |
||
| 456 | if v1.x > v2.x then Result.x := v1.x else Result.x := v2.x; |
||
| 457 | if v1.y > v2.y then Result.y := v1.y else Result.y := v2.y; |
||
| 458 | if v1.z > v2.z then Result.z := v1.z else Result.z := v2.z; |
||
| 459 | end; |
||
| 460 | |||
| 461 | function D3DMath_Vec3Scale(const v: TD3DVector; const s: TD3DValue): TD3DVector; |
||
| 462 | begin |
||
| 463 | Result.x := v.x * s; |
||
| 464 | Result.y := v.y * s; |
||
| 465 | Result.z := v.z * s; |
||
| 466 | end; |
||
| 467 | |||
| 468 | // Linear interpolation. V1 + s(V2-V1) |
||
| 469 | |||
| 470 | function D3DMath_Vec3Lerp(out vOut: TD3DVector; const v1, v2: TD3DVector; const s: TD3DValue): TD3DVector; |
||
| 471 | begin |
||
| 472 | Result.x := v1.x + s * (v2.x - v1.x); |
||
| 473 | Result.y := v1.y + s * (v2.y - v1.y); |
||
| 474 | Result.z := v1.z + s * (v2.z - v1.z); |
||
| 475 | end; |
||
| 476 | |||
| 477 | //----------------------------------------------------------------------------- |
||
| 478 | // File: D3DMath.cpp |
||
| 479 | // |
||
| 480 | // Desc: Shortcut macros and functions for using DX objects |
||
| 481 | // |
||
| 482 | // Copyright (c) 1997-1999 Microsoft Corporation. All rights reserved |
||
| 483 | //----------------------------------------------------------------------------- |
||
| 484 | |||
| 485 | function D3DMath_IsZero(a: Double; fTol: Double { = g_EPSILON}): Boolean; |
||
| 486 | begin |
||
| 487 | if a < 0 then |
||
| 488 | Result := a >= -fTol |
||
| 489 | else |
||
| 490 | Result := a <= fTol; |
||
| 491 | end; |
||
| 492 | |||
| 493 | //----------------------------------------------------------------------------- |
||
| 494 | // Name: D3DMath_MatrixMultiply() |
||
| 495 | // Desc: Does the matrix operation: [Q] = [A] * [B]. Note that the order of |
||
| 496 | // this operation was changed from the previous version of the DXSDK. |
||
| 497 | //----------------------------------------------------------------------------- |
||
| 498 | |||
| 499 | procedure D3DMath_MatrixMultiply(var q: TD3DMatrix; const a, b: TD3DMatrix); |
||
| 500 | type |
||
| 501 | PArrayD3DValue = ^TArrayD3DValue; |
||
| 502 | TArrayD3DValue = array[0..15] of TD3DValue; |
||
| 503 | var |
||
| 504 | pA, pB, pQ: PArrayD3DValue; |
||
| 505 | i, j, k: Integer; |
||
| 506 | qq: TD3DMatrix; |
||
| 507 | begin |
||
| 508 | FillChar(qq, SizeOf(qq), 0); |
||
| 509 | |||
| 510 | pA := @a; |
||
| 511 | pB := @b; |
||
| 512 | pQ := @qq; |
||
| 513 | for i := 0 to 3 do |
||
| 514 | for j := 0 to 3 do |
||
| 515 | for k := 0 to 3 do |
||
| 516 | pQ[4 * i + j] := pQ[4 * i + j] + pA[4 * i + k] * pB[4 * k + j]; |
||
| 517 | q := qq; {== protect of recurrence} |
||
| 518 | end; |
||
| 519 | |||
| 520 | function D3DMath_MatrixMultiply(const a, b: TD3DMatrix): TD3DMatrix; |
||
| 521 | begin |
||
| 522 | D3DMath_MatrixMultiply(Result, a, b); |
||
| 523 | end; |
||
| 524 | |||
| 525 | //----------------------------------------------------------------------------- |
||
| 526 | // Name: D3DMath_MatrixInvert() |
||
| 527 | // Desc: Does the matrix operation: [Q] = inv[A]. Note: this function only |
||
| 528 | // works for matrices with [0 0 0 1] for the 4th column. |
||
| 529 | //----------------------------------------------------------------------------- |
||
| 530 | |||
| 531 | function D3DMath_MatrixInvert(var q: TD3DMatrix; const a: TD3DMatrix): HResult; |
||
| 532 | var |
||
| 533 | fDetInv: Double; |
||
| 534 | begin |
||
| 535 | if (abs(a._44 - 1.0) > 0.001) or (abs(a._14) > 0.001) or (abs(a._24) > 0.001) or (abs(a._34) > 0.001) then |
||
| 536 | begin |
||
| 537 | Result := E_INVALIDARG; |
||
| 538 | Exit; |
||
| 539 | end; |
||
| 540 | |||
| 541 | fDetInv := 1.0 / (a._11 * (a._22 * a._33 - a._23 * a._32) - |
||
| 542 | a._12 * (a._21 * a._33 - a._23 * a._31) + |
||
| 543 | a._13 * (a._21 * a._32 - a._22 * a._31)); |
||
| 544 | |||
| 545 | q._11 := fDetInv * (a._22 * a._33 - a._23 * a._32); |
||
| 546 | q._12 := -fDetInv * (a._12 * a._33 - a._13 * a._32); |
||
| 547 | q._13 := fDetInv * (a._12 * a._23 - a._13 * a._22); |
||
| 548 | q._14 := 0.0; |
||
| 549 | |||
| 550 | q._21 := -fDetInv * (a._21 * a._33 - a._23 * a._31); |
||
| 551 | q._22 := fDetInv * (a._11 * a._33 - a._13 * a._31); |
||
| 552 | q._23 := -fDetInv * (a._11 * a._23 - a._13 * a._21); |
||
| 553 | q._24 := 0.0; |
||
| 554 | |||
| 555 | q._31 := fDetInv * (a._21 * a._32 - a._22 * a._31); |
||
| 556 | q._32 := -fDetInv * (a._11 * a._32 - a._12 * a._31); |
||
| 557 | q._33 := fDetInv * (a._11 * a._22 - a._12 * a._21); |
||
| 558 | q._34 := 0.0; |
||
| 559 | |||
| 560 | q._41 := -(a._41 * q._11 + a._42 * q._21 + a._43 * q._31); |
||
| 561 | q._42 := -(a._41 * q._12 + a._42 * q._22 + a._43 * q._32); |
||
| 562 | q._43 := -(a._41 * q._13 + a._42 * q._23 + a._43 * q._33); |
||
| 563 | q._44 := 1.0; |
||
| 564 | |||
| 565 | Result := S_OK; |
||
| 566 | end; |
||
| 567 | |||
| 568 | function D3DMath_MatrixInvert(const a: TD3DMatrix): TD3DMatrix; |
||
| 569 | begin |
||
| 570 | if D3DMath_MatrixInvert(Result, a) <> S_OK then |
||
| 571 | FillChar(Result, SizeOf(Result), 0); |
||
| 572 | end; |
||
| 573 | |||
| 574 | //----------------------------------------------------------------------------- |
||
| 575 | // Name: D3DMath_VectorMatrixMultiply() |
||
| 576 | // Desc: Multiplies a vector by a matrix |
||
| 577 | //----------------------------------------------------------------------------- |
||
| 578 | |||
| 579 | function D3DMath_VectorMatrixMultiply(var vDest: TD3DVector; const vSrc: TD3DVector; |
||
| 580 | const mat: TD3DMatrix): HResult; |
||
| 581 | var |
||
| 582 | x, y, z, w: Double; |
||
| 583 | begin |
||
| 584 | x := vSrc.x * mat._11 + vSrc.y * mat._21 + vSrc.z * mat._31 + mat._41; |
||
| 585 | y := vSrc.x * mat._12 + vSrc.y * mat._22 + vSrc.z * mat._32 + mat._42; |
||
| 586 | z := vSrc.x * mat._13 + vSrc.y * mat._23 + vSrc.z * mat._33 + mat._43; |
||
| 587 | w := vSrc.x * mat._14 + vSrc.y * mat._24 + vSrc.z * mat._34 + mat._44; |
||
| 588 | |||
| 589 | if abs(w) < g_EPSILON then |
||
| 590 | begin |
||
| 591 | Result := E_INVALIDARG; |
||
| 592 | Exit; |
||
| 593 | end; |
||
| 594 | |||
| 595 | vDest.x := x / w; |
||
| 596 | vDest.y := y / w; |
||
| 597 | vDest.z := z / w; |
||
| 598 | |||
| 599 | Result := S_OK; |
||
| 600 | end; |
||
| 601 | |||
| 602 | //----------------------------------------------------------------------------- |
||
| 603 | // Name: D3DMath_VertexMatrixMultiply() |
||
| 604 | // Desc: Multiplies a vertex by a matrix |
||
| 605 | //----------------------------------------------------------------------------- |
||
| 606 | |||
| 607 | function D3DMath_VertexMatrixMultiply(var vDest: TD3DVertex; const vSrc: TD3DVertex; |
||
| 608 | const mat: TD3DMatrix): HResult; |
||
| 609 | var |
||
| 610 | pSrcVec, pDestVec: PD3DVector; |
||
| 611 | begin |
||
| 612 | pSrcVec := @vSrc.x; |
||
| 613 | pDestVec := @vDest.x; |
||
| 614 | |||
| 615 | Result := D3DMath_VectorMatrixMultiply(pDestVec^, pSrcVec^, mat); |
||
| 616 | if SUCCEEDED(Result) then |
||
| 617 | begin |
||
| 618 | pSrcVec := @vSrc.nx; |
||
| 619 | pDestVec := @vDest.nx; |
||
| 620 | Result := D3DMath_VectorMatrixMultiply(pDestVec^, pSrcVec^, mat); |
||
| 621 | end; |
||
| 622 | end; |
||
| 623 | |||
| 624 | //----------------------------------------------------------------------------- |
||
| 625 | // Name: D3DMath_QuaternionFromRotation() |
||
| 626 | // Desc: Converts a normalized axis and angle to a unit quaternion. |
||
| 627 | //----------------------------------------------------------------------------- |
||
| 628 | |||
| 629 | procedure D3DMath_QuaternionFromRotation(var x, y, z, w: Double; |
||
| 630 | const v: TD3DVector; fTheta: Double); |
||
| 631 | begin |
||
| 632 | x := sin(fTheta / 2.0) * v.x; |
||
| 633 | y := sin(fTheta / 2.0) * v.y; |
||
| 634 | z := sin(fTheta / 2.0) * v.z; |
||
| 635 | w := cos(fTheta / 2.0); |
||
| 636 | end; |
||
| 637 | |||
| 638 | function D3DMath_QuaternionFromRotation(const axis: TD3DVector; const r: Double): TQuaternion; |
||
| 639 | var |
||
| 640 | // r: Integer; |
||
| 641 | a: TD3DVector; |
||
| 642 | begin |
||
| 643 | // r := (t div 2) and $FFF; |
||
| 644 | a := VectorNormalize(axis); |
||
| 645 | Result.X := a.X * Sin(R); |
||
| 646 | Result.Y := a.Y * Sin(R); |
||
| 647 | Result.Z := a.Z * Sin(R); |
||
| 648 | Result.W := Cos(R); |
||
| 649 | end; |
||
| 650 | |||
| 651 | //----------------------------------------------------------------------------- |
||
| 652 | // Name: D3DMath_RotationFromQuaternion() |
||
| 653 | // Desc: Converts a normalized axis and angle to a unit quaternion. |
||
| 654 | //----------------------------------------------------------------------------- |
||
| 655 | |||
| 656 | procedure D3DMath_RotationFromQuaternion(var v: TD3DVector; var fTheta: Double; |
||
| 657 | x, y, z, w: Double); |
||
| 658 | begin |
||
| 659 | fTheta := ArcCos(w) * 2.0; |
||
| 660 | v.x := x / sin(fTheta / 2.0); |
||
| 661 | v.y := y / sin(fTheta / 2.0); |
||
| 662 | v.z := z / sin(fTheta / 2.0); |
||
| 663 | end; |
||
| 664 | |||
| 665 | //----------------------------------------------------------------------------- |
||
| 666 | // Name: D3DMath_QuaternionFromAngles() |
||
| 667 | // Desc: Converts euler angles to a unit quaternion. |
||
| 668 | //----------------------------------------------------------------------------- |
||
| 669 | |||
| 670 | procedure D3DMath_QuaternionFromAngles(var x, y, z, w: Double; fYaw, fPitch, fRoll: Double); |
||
| 671 | var |
||
| 672 | fSinYaw, fSinPitch, fSinRoll, fCosYaw, fCosPitch, fCosRoll: Double; |
||
| 673 | begin |
||
| 674 | fSinYaw := sin(fYaw / 2.0); |
||
| 675 | fSinPitch := sin(fPitch / 2.0); |
||
| 676 | fSinRoll := sin(fRoll / 2.0); |
||
| 677 | fCosYaw := cos(fYaw / 2.0); |
||
| 678 | fCosPitch := cos(fPitch / 2.0); |
||
| 679 | fCosRoll := cos(fRoll / 2.0); |
||
| 680 | |||
| 681 | x := fSinRoll * fCosPitch * fCosYaw - fCosRoll * fSinPitch * fSinYaw; |
||
| 682 | y := fCosRoll * fSinPitch * fCosYaw + fSinRoll * fCosPitch * fSinYaw; |
||
| 683 | z := fCosRoll * fCosPitch * fSinYaw - fSinRoll * fSinPitch * fCosYaw; |
||
| 684 | w := fCosRoll * fCosPitch * fCosYaw + fSinRoll * fSinPitch * fSinYaw; |
||
| 685 | end; |
||
| 686 | |||
| 687 | //----------------------------------------------------------------------------- |
||
| 688 | // Name: D3DMath_MatrixFromQuaternion() |
||
| 689 | // Desc: Converts a unit quaternion into a rotation matrix. |
||
| 690 | //----------------------------------------------------------------------------- |
||
| 691 | |||
| 692 | procedure D3DMath_MatrixFromQuaternion(var mat: TD3DMatrix; x, y, z, w: Double); |
||
| 693 | var |
||
| 694 | xx, yy, zz, xy, xz, yz, wx, wy, wz: Double; |
||
| 695 | begin |
||
| 696 | xx := x * x; yy := y * y; zz := z * z; |
||
| 697 | xy := x * y; xz := x * z; yz := y * z; |
||
| 698 | wx := w * x; wy := w * y; wz := w * z; |
||
| 699 | |||
| 700 | mat._11 := 1 - 2 * (yy + zz); |
||
| 701 | mat._12 := 2 * (xy - wz); |
||
| 702 | mat._13 := 2 * (xz + wy); |
||
| 703 | |||
| 704 | mat._21 := 2 * (xy + wz); |
||
| 705 | mat._22 := 1 - 2 * (xx + zz); |
||
| 706 | mat._23 := 2 * (yz - wx); |
||
| 707 | |||
| 708 | mat._31 := 2 * (xz - wy); |
||
| 709 | mat._32 := 2 * (yz + wx); |
||
| 710 | mat._33 := 1 - 2 * (xx + yy); |
||
| 711 | |||
| 712 | mat._14 := 0.0; mat._24 := 0.0; mat._34 := 0.0; |
||
| 713 | mat._41 := 0.0; mat._42 := 0.0; mat._43 := 0.0; |
||
| 714 | mat._44 := 1.0; |
||
| 715 | end; |
||
| 716 | |||
| 717 | function D3DMath_MatrixFromQuaternion(q: TQuaternion): TD3DMatrix; |
||
| 718 | begin |
||
| 719 | D3DMath_MatrixFromQuaternion(Result, q.X, q.Y, q.Z, q.W) |
||
| 720 | end; |
||
| 721 | |||
| 722 | //----------------------------------------------------------------------------- |
||
| 723 | // Name: D3DMath_QuaternionFromMatrix() |
||
| 724 | // Desc: Converts a rotation matrix into a unit quaternion. |
||
| 725 | //----------------------------------------------------------------------------- |
||
| 726 | |||
| 727 | procedure D3DMath_QuaternionFromMatrix(var x, y, z, w: Double; var mat: TD3DMatrix); |
||
| 728 | var |
||
| 729 | s: Double; |
||
| 730 | xx, yy, zz, xy, xz, yz, wx, wy, wz: Double; |
||
| 731 | begin |
||
| 732 | if (mat._11 + mat._22 + mat._33 > 0.0) then |
||
| 733 | begin |
||
| 734 | s := sqrt(mat._11 + mat._22 + mat._33 + mat._44); |
||
| 735 | |||
| 736 | x := (mat._23 - mat._32) / (2 * s); |
||
| 737 | y := (mat._31 - mat._13) / (2 * s); |
||
| 738 | z := (mat._12 - mat._21) / (2 * s); |
||
| 739 | w := 0.5 * s; |
||
| 740 | end; |
||
| 741 | |||
| 742 | xx := x * x; yy := y * y; zz := z * z; |
||
| 743 | xy := x * y; xz := x * z; yz := y * z; |
||
| 744 | wx := w * x; wy := w * y; wz := w * z; |
||
| 745 | |||
| 746 | mat._11 := 1 - 2 * (yy + zz); |
||
| 747 | mat._12 := 2 * (xy - wz); |
||
| 748 | mat._13 := 2 * (xz + wy); |
||
| 749 | |||
| 750 | mat._21 := 2 * (xy + wz); |
||
| 751 | mat._22 := 1 - 2 * (xx + zz); |
||
| 752 | mat._23 := 2 * (yz - wx); |
||
| 753 | |||
| 754 | mat._31 := 2 * (xz - wy); |
||
| 755 | mat._32 := 2 * (yz + wx); |
||
| 756 | mat._33 := 1 - 2 * (xx + yy); |
||
| 757 | |||
| 758 | mat._14 := 0.0; mat._24 := 0.0; mat._34 := 0.0; |
||
| 759 | mat._41 := 0.0; mat._42 := 0.0; mat._43 := 0.0; |
||
| 760 | mat._44 := 1.0; |
||
| 761 | end; |
||
| 762 | |||
| 763 | //----------------------------------------------------------------------------- |
||
| 764 | // Name: D3DMath_QuaternionMultiply() |
||
| 765 | // Desc: Mulitples two quaternions together as in {Q} = {A} * {B}. |
||
| 766 | //----------------------------------------------------------------------------- |
||
| 767 | |||
| 768 | procedure D3DMath_QuaternionMultiply(var Qx, Qy, Qz, Qw: Double; |
||
| 769 | Ax, Ay, Az, Aw, Bx, By, Bz, Bw: Double); |
||
| 770 | var |
||
| 771 | Dx, Dy, Dz, Dw: Double; |
||
| 772 | begin |
||
| 773 | Dx := Ax * Bw + Ay * Bz - Az * By + Aw * Bx; |
||
| 774 | Dy := -Ax * Bz + Ay * Bw + Az * Bx + Aw * By; |
||
| 775 | Dz := Ax * By - Ay * Bx + Az * Bw + Aw * Bz; |
||
| 776 | Dw := -Ax * Bx - Ay * By - Az * Bz + Aw * Bw; |
||
| 777 | |||
| 778 | Qx := Dx; Qy := Dy; Qz := Dz; Qw := Dw; |
||
| 779 | end; |
||
| 780 | |||
| 781 | function D3DMath_QuaternionMultiply(a, b: TQuaternion): TQuaternion; |
||
| 782 | var |
||
| 783 | Qx, Qy, Qz, Qw: Double; |
||
| 784 | begin |
||
| 785 | D3DMath_QuaternionMultiply(Qx, Qy, Qz, Qw, A.x, A.y, A.z, A.w, B.x, B.y, B.z, B.w); |
||
| 786 | Result.X := Qx; |
||
| 787 | Result.Y := Qy; |
||
| 788 | Result.Z := Qz; |
||
| 789 | Result.W := Qw; |
||
| 790 | end; |
||
| 791 | |||
| 792 | //----------------------------------------------------------------------------- |
||
| 793 | // Name: D3DMath_SlerpQuaternions() |
||
| 794 | // Desc: Compute a quaternion which is the spherical linear interpolation |
||
| 795 | // between two other quaternions by dvFraction. |
||
| 796 | //----------------------------------------------------------------------------- |
||
| 797 | |||
| 798 | procedure D3DMath_QuaternionSlerp(var Qx, Qy, Qz, Qw: Double; |
||
| 799 | Ax, Ay, Az, Aw, Bx, By, Bz, Bw, fAlpha: Double); |
||
| 800 | var |
||
| 801 | fCosTheta: Double; |
||
| 802 | fBeta: Double; |
||
| 803 | fTheta: Double; |
||
| 804 | begin |
||
| 805 | // Compute dot product (equal to cosine of the angle between quaternions) |
||
| 806 | fCosTheta := Ax * Bx + Ay * By + Az * Bz + Aw * Bw; |
||
| 807 | |||
| 808 | // Check angle to see if quaternions are in opposite hemispheres |
||
| 809 | if fCosTheta < 0.0 then |
||
| 810 | begin |
||
| 811 | // If so, flip one of the quaterions |
||
| 812 | fCosTheta := -fCosTheta; |
||
| 813 | Bx := -Bx; By := -By; Bz := -Bz; Bw := -Bw; |
||
| 814 | end; |
||
| 815 | |||
| 816 | // Set factors to do linear interpolation, as a special case where the |
||
| 817 | // quaternions are close together. |
||
| 818 | fBeta := 1.0 - fAlpha; |
||
| 819 | |||
| 820 | // If the quaternions aren't close, proceed with spherical interpolation |
||
| 821 | if 1.0 - fCosTheta > 0.001 then |
||
| 822 | begin |
||
| 823 | fTheta := arccos(fCosTheta); |
||
| 824 | |||
| 825 | fBeta := sin(fTheta * fBeta) / sin(fTheta); |
||
| 826 | fAlpha := sin(fTheta * fAlpha) / sin(fTheta); |
||
| 827 | end; |
||
| 828 | |||
| 829 | // Do the interpolation |
||
| 830 | Qx := fBeta * Ax + fAlpha * Bx; |
||
| 831 | Qy := fBeta * Ay + fAlpha * By; |
||
| 832 | Qz := fBeta * Az + fAlpha * Bz; |
||
| 833 | Qw := fBeta * Aw + fAlpha * Bw; |
||
| 834 | end; |
||
| 835 | |||
| 836 | function D3DMath_QuaternionSlerp(A, B: TQuaternion; fAlpha: Double): TQuaternion; |
||
| 837 | var |
||
| 838 | Qx, Qy, Qz, Qw: Double; |
||
| 839 | begin |
||
| 840 | D3DMath_QuaternionSlerp(Qx, Qy, Qz, Qw, A.x, A.y, A.z, A.w, B.x, B.y, B.z, B.w, fAlpha); |
||
| 841 | Result.X := Qx; |
||
| 842 | Result.Y := Qy; |
||
| 843 | Result.Z := Qz; |
||
| 844 | Result.W := Qw; |
||
| 845 | end; |
||
| 846 | |||
| 847 | //----------------------------------------------------------------------------- |
||
| 848 | // File: D3DUtil.cpp |
||
| 849 | // |
||
| 850 | // Desc: Shortcut macros and functions for using DX objects |
||
| 851 | // |
||
| 852 | // |
||
| 853 | // Copyright (c) 1997-1999 Microsoft Corporation. All rights reserved |
||
| 854 | //----------------------------------------------------------------------------- |
||
| 855 | |||
| 856 | //----------------------------------------------------------------------------- |
||
| 857 | // Name: D3DUtil_InitSurfaceDesc() |
||
| 858 | // Desc: Helper function called to build a DDSURFACEDESC2 structure, |
||
| 859 | // typically before calling CreateSurface() or GetSurfaceDesc() |
||
| 860 | //----------------------------------------------------------------------------- |
||
| 861 | |||
| 862 | procedure D3DUtil_InitSurfaceDesc(var ddsd: TDDSurfaceDesc2; dwFlags, dwCaps: DWORD); |
||
| 863 | begin |
||
| 864 | FillChar(ddsd, SizeOf(ddsd), 0); |
||
| 865 | ddsd.dwSize := SizeOf(ddsd); |
||
| 866 | ddsd.dwFlags := dwFlags; |
||
| 867 | ddsd.ddsCaps.dwCaps := dwCaps; |
||
| 868 | ddsd.ddpfPixelFormat.dwSize := SizeOf(ddsd.ddpfPixelFormat); |
||
| 869 | end; |
||
| 870 | |||
| 871 | //----------------------------------------------------------------------------- |
||
| 872 | // Name: D3DUtil_InitMaterial() |
||
| 873 | // Desc: Helper function called to build a D3DMATERIAL7 structure |
||
| 874 | //----------------------------------------------------------------------------- |
||
| 875 | |||
| 876 | procedure D3DUtil_InitMaterial(var mtrl: TD3DMaterial7; r, g, b, a: Double); |
||
| 877 | begin |
||
| 878 | FillChar(mtrl, SizeOf(mtrl), 0); |
||
| 879 | mtrl.dcvDiffuse.r := r; mtrl.dcvAmbient.r := r; |
||
| 880 | mtrl.dcvDiffuse.g := g; mtrl.dcvAmbient.g := g; |
||
| 881 | mtrl.dcvDiffuse.b := b; mtrl.dcvAmbient.b := b; |
||
| 882 | mtrl.dcvDiffuse.a := a; mtrl.dcvAmbient.a := a; |
||
| 883 | end; |
||
| 884 | |||
| 885 | //----------------------------------------------------------------------------- |
||
| 886 | // Name: D3DUtil_InitLight() |
||
| 887 | // Desc: Initializes a D3DLIGHT7 structure |
||
| 888 | //----------------------------------------------------------------------------- |
||
| 889 | |||
| 890 | procedure D3DUtil_InitLight(var light: TD3DLight7; ltType: TD3DLightType; x, y, z: Double); |
||
| 891 | begin |
||
| 892 | FillChar(light, SizeOf(light), 0); |
||
| 893 | light.dltType := ltType; |
||
| 894 | light.dcvDiffuse.r := 1.0; |
||
| 895 | light.dcvDiffuse.g := 1.0; |
||
| 896 | light.dcvDiffuse.b := 1.0; |
||
| 897 | light.dcvSpecular := light.dcvDiffuse; |
||
| 898 | light.dvPosition.x := x; light.dvDirection.x := x; |
||
| 899 | light.dvPosition.y := y; light.dvDirection.y := y; |
||
| 900 | light.dvPosition.z := z; light.dvDirection.z := z; |
||
| 901 | light.dvAttenuation0 := 1.0; |
||
| 902 | light.dvRange := D3DLIGHT_RANGE_MAX; |
||
| 903 | end; |
||
| 904 | |||
| 905 | procedure D3DUtil_SetIdentityMatrix(out m: TD3DMatrix); |
||
| 906 | begin |
||
| 907 | m._12 := 0; m._13 := 0; m._14 := 0; m._21 := 0; m._23 := 0; m._24 := 0; |
||
| 908 | m._31 := 0; m._32 := 0; m._34 := 0; m._41 := 0; m._42 := 0; m._43 := 0; |
||
| 909 | m._11 := 1; m._22 := 1; m._33 := 1; m._44 := 1; |
||
| 910 | end; |
||
| 911 | |||
| 912 | function D3DUtil_SetIdentityMatrix: TD3DMatrix; |
||
| 913 | begin |
||
| 914 | D3DUtil_SetIdentityMatrix(Result); |
||
| 915 | end; |
||
| 916 | |||
| 917 | function D3DUtil_SetScaleMatrix(const x, y, z: Single): TD3DMatrix; |
||
| 918 | begin |
||
| 919 | with Result do |
||
| 920 | begin |
||
| 921 | _11 := x; _12 := 0; _13 := 0; _14 := 0; |
||
| 922 | _21 := 0; _22 := y; _23 := 0; _24 := 0; |
||
| 923 | _31 := 0; _32 := 0; _33 := z; _34 := 0; |
||
| 924 | _41 := 0; _42 := 0; _43 := 0; _44 := 1; |
||
| 925 | end; |
||
| 926 | end; |
||
| 927 | |||
| 928 | //----------------------------------------------------------------------------- |
||
| 929 | // Name: D3DUtil_SetViewMatrix() |
||
| 930 | // Desc: Given an eye point, a lookat point, and an up vector, this |
||
| 931 | // function builds a 4x4 view matrix. |
||
| 932 | //----------------------------------------------------------------------------- |
||
| 933 | |||
| 934 | function D3DUtil_SetViewMatrix(var mat: TD3DMatrix; const vFrom, vAt, vWorldUp: TD3DVector): HResult; |
||
| 935 | var |
||
| 936 | vView: TD3DVector; |
||
| 937 | fLength: Double; |
||
| 938 | fDotProduct: Double; |
||
| 939 | vUp: TD3DVector; |
||
| 940 | vRight: TD3DVector; |
||
| 941 | begin |
||
| 942 | // Get the z basis vector, which points straight ahead. This is the |
||
| 943 | // difference from the eyepoint to the lookat point. |
||
| 944 | vView := VectorSub(vAt, vFrom); |
||
| 945 | |||
| 946 | fLength := VectorMagnitude(vView); |
||
| 947 | if fLength < 0.1E-6 then |
||
| 948 | begin |
||
| 949 | Result := E_INVALIDARG; |
||
| 950 | Exit; |
||
| 951 | end; |
||
| 952 | |||
| 953 | // Normalize the z basis vector |
||
| 954 | vView := VectorDivS(vView, fLength); |
||
| 955 | |||
| 956 | // Get the dot product, and calculate the projection of the z basis |
||
| 957 | // vector onto the up vector. The projection is the y basis vector. |
||
| 958 | fDotProduct := VectorDotProduct(vWorldUp, vView); |
||
| 959 | |||
| 960 | vUp := VectorSub(vWorldUp, VectorMulS(vView, fDotProduct)); |
||
| 961 | |||
| 962 | // If this vector has near-zero length because the input specified a |
||
| 963 | // bogus up vector, let's try a default up vector |
||
| 964 | fLength := VectorMagnitude(vUp); |
||
| 965 | if 1E-6 > fLength then |
||
| 966 | begin |
||
| 967 | vUp := VectorSub(MakeD3DVector(0, 1, 0), VectorMulS(vView, vView.y)); |
||
| 968 | |||
| 969 | // If we still have near-zero length, resort to a different axis. |
||
| 970 | fLength := VectorMagnitude(vUp); |
||
| 971 | if 1E-6 > fLength then |
||
| 972 | begin |
||
| 973 | vUp := VectorSub(MakeD3DVector(0, 0, 1), VectorMulS(vView, vView.z)); |
||
| 974 | |||
| 975 | fLength := VectorMagnitude(vUp); |
||
| 976 | if 1E-6 > fLength then |
||
| 977 | begin |
||
| 978 | Result := E_INVALIDARG; |
||
| 979 | Exit; |
||
| 980 | end; |
||
| 981 | end; |
||
| 982 | end; |
||
| 983 | |||
| 984 | // Normalize the y basis vector |
||
| 985 | vUp := VectorDivS(vUp, fLength); |
||
| 986 | |||
| 987 | // The x basis vector is found simply with the cross product of the y |
||
| 988 | // and z basis vectors |
||
| 989 | vRight := VectorCrossProduct(vUp, vView); |
||
| 990 | |||
| 991 | // Start building the matrix. The first three rows contains the basis |
||
| 992 | // vectors used to rotate the view to point at the lookat point |
||
| 993 | D3DUtil_SetIdentityMatrix(mat); |
||
| 994 | mat._11 := vRight.x; mat._12 := vUp.x; mat._13 := vView.x; |
||
| 995 | mat._21 := vRight.y; mat._22 := vUp.y; mat._23 := vView.y; |
||
| 996 | mat._31 := vRight.z; mat._32 := vUp.z; mat._33 := vView.z; |
||
| 997 | |||
| 998 | // Do the translation values (rotations are still about the eyepoint) |
||
| 999 | mat._41 := -VectorDotProduct(vFrom, vRight); |
||
| 1000 | mat._42 := -VectorDotProduct(vFrom, vUp); |
||
| 1001 | mat._43 := -VectorDotProduct(vFrom, vView); |
||
| 1002 | |||
| 1003 | Result := S_OK; |
||
| 1004 | end; |
||
| 1005 | |||
| 1006 | //----------------------------------------------------------------------------- |
||
| 1007 | // Name: D3DUtil_SetProjectionMatrix() |
||
| 1008 | // Desc: Sets the passed in 4x4 matrix to a perpsective projection matrix built |
||
| 1009 | // from the field-of-view (fov, in y), aspect ratio, near plane (D), |
||
| 1010 | // and far plane (F). Note that the projection matrix is normalized for |
||
| 1011 | // element [3][4] to be 1.0. This is performed so that W-based range fog |
||
| 1012 | // will work correctly. |
||
| 1013 | //----------------------------------------------------------------------------- |
||
| 1014 | |||
| 1015 | function D3DUtil_SetProjectionMatrix(var mat: TD3DMatrix; fFOV, fAspect, fNearPlane, fFarPlane: Double): HResult; |
||
| 1016 | var |
||
| 1017 | w, h, Q: Double; |
||
| 1018 | begin |
||
| 1019 | if (abs(fFarPlane - fNearPlane) < 0.01) or (abs(sin(fFOV / 2)) < 0.01) then |
||
| 1020 | begin |
||
| 1021 | Result := E_INVALIDARG; |
||
| 1022 | Exit; |
||
| 1023 | end; |
||
| 1024 | |||
| 1025 | w := fAspect * (cos(fFOV / 2) / sin(fFOV / 2)); |
||
| 1026 | h := 1.0 * (cos(fFOV / 2) / sin(fFOV / 2)); |
||
| 1027 | Q := fFarPlane / (fFarPlane - fNearPlane); |
||
| 1028 | |||
| 1029 | FillChar(mat, SizeOf(mat), 0); |
||
| 1030 | mat._11 := w; |
||
| 1031 | mat._22 := h; |
||
| 1032 | mat._33 := Q; |
||
| 1033 | mat._34 := 1.0; |
||
| 1034 | mat._43 := -Q * fNearPlane; |
||
| 1035 | |||
| 1036 | Result := S_OK; |
||
| 1037 | end; |
||
| 1038 | |||
| 1039 | //----------------------------------------------------------------------------- |
||
| 1040 | // Name: D3DUtil_SetRotateXMatrix() |
||
| 1041 | // Desc: Create Rotation matrix about X axis |
||
| 1042 | //----------------------------------------------------------------------------- |
||
| 1043 | |||
| 1044 | procedure D3DUtil_SetRotateXMatrix(var mat: TD3DMatrix; fRads: Double); |
||
| 1045 | begin |
||
| 1046 | D3DUtil_SetIdentityMatrix(mat); |
||
| 1047 | mat._22 := cos(fRads); |
||
| 1048 | mat._23 := sin(fRads); |
||
| 1049 | mat._32 := -sin(fRads); |
||
| 1050 | mat._33 := cos(fRads); |
||
| 1051 | end; |
||
| 1052 | |||
| 1053 | function D3DUtil_SetRotateXMatrix(fRads: Double): TD3DMatrix; |
||
| 1054 | begin |
||
| 1055 | D3DUtil_SetRotateXMatrix(Result, fRads); |
||
| 1056 | end; |
||
| 1057 | |||
| 1058 | //----------------------------------------------------------------------------- |
||
| 1059 | // Name: D3DUtil_SetRotateYMatrix() |
||
| 1060 | // Desc: Create Rotation matrix about Y axis |
||
| 1061 | //----------------------------------------------------------------------------- |
||
| 1062 | |||
| 1063 | procedure D3DUtil_SetRotateYMatrix(var mat: TD3DMatrix; fRads: Double); |
||
| 1064 | begin |
||
| 1065 | D3DUtil_SetIdentityMatrix(mat); |
||
| 1066 | mat._11 := cos(fRads); |
||
| 1067 | mat._13 := -sin(fRads); |
||
| 1068 | mat._31 := sin(fRads); |
||
| 1069 | mat._33 := cos(fRads); |
||
| 1070 | end; |
||
| 1071 | |||
| 1072 | function D3DUtil_SetRotateYMatrix(fRads: Double): TD3DMatrix; |
||
| 1073 | begin |
||
| 1074 | D3DUtil_SetRotateYMatrix(Result, fRads); |
||
| 1075 | end; |
||
| 1076 | |||
| 1077 | //----------------------------------------------------------------------------- |
||
| 1078 | // Name: D3DUtil_SetRotateZMatrix() |
||
| 1079 | // Desc: Create Rotation matrix about Z axis |
||
| 1080 | //----------------------------------------------------------------------------- |
||
| 1081 | |||
| 1082 | procedure D3DUtil_SetRotateZMatrix(var mat: TD3DMatrix; fRads: Double); |
||
| 1083 | begin |
||
| 1084 | D3DUtil_SetIdentityMatrix(mat); |
||
| 1085 | mat._11 := cos(fRads); |
||
| 1086 | mat._12 := sin(fRads); |
||
| 1087 | mat._21 := -sin(fRads); |
||
| 1088 | mat._22 := cos(fRads); |
||
| 1089 | end; |
||
| 1090 | |||
| 1091 | function D3DUtil_SetRotateZMatrix(fRads: Double): TD3DMatrix; |
||
| 1092 | begin |
||
| 1093 | D3DUtil_SetRotateZMatrix(Result, fRads); |
||
| 1094 | end; |
||
| 1095 | |||
| 1096 | //----------------------------------------------------------------------------- |
||
| 1097 | // Name: D3DUtil_SetRotationMatrix |
||
| 1098 | // Desc: Create a Rotation matrix about vector direction |
||
| 1099 | //----------------------------------------------------------------------------- |
||
| 1100 | |||
| 1101 | procedure D3DUtil_SetRotationMatrix(var mat: TD3DMatrix; var vDir: TD3DVector; fRads: Double); |
||
| 1102 | var |
||
| 1103 | fCos, fSin: Double; |
||
| 1104 | v: TD3DVector; |
||
| 1105 | begin |
||
| 1106 | fCos := cos(fRads); |
||
| 1107 | fSin := sin(fRads); |
||
| 1108 | v := VectorNormalize(vDir); |
||
| 1109 | |||
| 1110 | mat._11 := (v.x * v.x) * (1.0 - fCos) + fCos; |
||
| 1111 | mat._12 := (v.x * v.y) * (1.0 - fCos) - (v.z * fSin); |
||
| 1112 | mat._13 := (v.x * v.z) * (1.0 - fCos) + (v.y * fSin); |
||
| 1113 | |||
| 1114 | mat._21 := (v.y * v.x) * (1.0 - fCos) + (v.z * fSin); |
||
| 1115 | mat._22 := (v.y * v.y) * (1.0 - fCos) + fCos; |
||
| 1116 | mat._23 := (v.y * v.z) * (1.0 - fCos) - (v.x * fSin); |
||
| 1117 | |||
| 1118 | mat._31 := (v.z * v.x) * (1.0 - fCos) - (v.y * fSin); |
||
| 1119 | mat._32 := (v.z * v.y) * (1.0 - fCos) + (v.x * fSin); |
||
| 1120 | mat._33 := (v.z * v.z) * (1.0 - fCos) + fCos; |
||
| 1121 | |||
| 1122 | mat._14 := 0; mat._24 := 0; mat._34 := 0; |
||
| 1123 | mat._41 := 0; mat._42 := 0; mat._43 := 0; |
||
| 1124 | mat._44 := 1.0; |
||
| 1125 | end; |
||
| 1126 | |||
| 1127 | function D3DUtil_SetRotationMatrixByX(const a: TD3DVector; const r: Double): TD3DVector; |
||
| 1128 | begin |
||
| 1129 | Result.X := a.X; |
||
| 1130 | Result.Y := a.Y * Cos(r) + a.Z * Sin(r); |
||
| 1131 | Result.Z := -a.Y * Sin(r) + a.Z * Cos(r); |
||
| 1132 | end; |
||
| 1133 | |||
| 1134 | function D3DUtil_SetRotationMatrixByY(const a: TD3DVector; const r: Double): TD3DVector; |
||
| 1135 | begin |
||
| 1136 | Result.X := a.X * Cos(r) - a.Z * Sin(r); |
||
| 1137 | Result.Y := a.Y; |
||
| 1138 | Result.Z := a.X * Sin(r) + a.Z * Cos(r); |
||
| 1139 | end; |
||
| 1140 | |||
| 1141 | function D3DUtil_SetRotationMatrixByZ(const a: TD3DVector; const r: Double): TD3DVector; |
||
| 1142 | begin |
||
| 1143 | Result.X := a.X * Cos(r) + a.Y * Sin(r); |
||
| 1144 | Result.Y := -a.X * Sin(r) + a.Y * Cos(r); |
||
| 1145 | Result.Z := a.Z; |
||
| 1146 | end; |
||
| 1147 | |||
| 1148 | // simple D2D operation |
||
| 1149 | |||
| 1150 | function D2DMath_VecAdd(const a: TD2DVector; const b: TD2DVector): TD2DVector; |
||
| 1151 | begin |
||
| 1152 | Result.X := a.X + b.X; |
||
| 1153 | Result.Y := a.Y + b.Y; |
||
| 1154 | end; |
||
| 1155 | |||
| 1156 | function D2DMath_VecSub(const a: TD2DVector; const b: TD2DVector): TD2DVector; |
||
| 1157 | begin |
||
| 1158 | Result.X := a.X - b.X; |
||
| 1159 | Result.Y := a.Y - b.Y; |
||
| 1160 | end; |
||
| 1161 | |||
| 1162 | function D2DMath_VecDotProduct(const a, b: TD2DVector): Single; |
||
| 1163 | begin |
||
| 1164 | Result := a.X * b.X + a.Y * b.Y; |
||
| 1165 | end; |
||
| 1166 | |||
| 1167 | function D2DMath_VecDistance(const a, b: TD2DVector): Single; |
||
| 1168 | begin |
||
| 1169 | Result := sqrt(SQR(a.X - b.X) + SQR(a.Y - b.Y)); |
||
| 1170 | end; |
||
| 1171 | |||
| 1172 | function D2DMath_VecLength(const a: TD2DVector): Single; |
||
| 1173 | begin |
||
| 1174 | Result := sqrt(SQR(a.X) + SQR(a.Y)); |
||
| 1175 | end; |
||
| 1176 | |||
| 1177 | function D2DMath_VecNormalize(const a: TD2DVector): TD2DVector; |
||
| 1178 | var |
||
| 1179 | len: Single; |
||
| 1180 | begin |
||
| 1181 | len := D2DMath_VecLength(a); |
||
| 1182 | if len = 0 then |
||
| 1183 | begin |
||
| 1184 | result := MakeD2DVector(0, 0); |
||
| 1185 | Exit; |
||
| 1186 | end; |
||
| 1187 | |||
| 1188 | result.X := a.X / len; |
||
| 1189 | result.Y := a.Y / len; |
||
| 1190 | end; |
||
| 1191 | |||
| 1192 | function D2DMath_VecToAngle(const a: TD2DVector): Double; |
||
| 1193 | var |
||
| 1194 | v: TD2DVector; |
||
| 1195 | sg: Integer; |
||
| 1196 | hi, lo, mid: Integer; |
||
| 1197 | begin |
||
| 1198 | Result := 0.0; |
||
| 1199 | |||
| 1200 | v := D2DMath_VecNormalize(a); |
||
| 1201 | |||
| 1202 | if (v.y > 0) then |
||
| 1203 | begin |
||
| 1204 | if v.x > 0 then |
||
| 1205 | sg := 1 |
||
| 1206 | else |
||
| 1207 | begin |
||
| 1208 | sg := 2; |
||
| 1209 | v.x := -v.x; |
||
| 1210 | end; |
||
| 1211 | end |
||
| 1212 | else |
||
| 1213 | if (v.y < 0) then |
||
| 1214 | begin |
||
| 1215 | if v.x >= 0 then |
||
| 1216 | sg := 4 |
||
| 1217 | else |
||
| 1218 | begin |
||
| 1219 | sg := 3; |
||
| 1220 | v.x := -v.x; |
||
| 1221 | end; |
||
| 1222 | end |
||
| 1223 | else |
||
| 1224 | begin |
||
| 1225 | if v.x >= 0 then |
||
| 1226 | sg := 1 |
||
| 1227 | else |
||
| 1228 | begin |
||
| 1229 | sg := 3; |
||
| 1230 | v.x := -v.x; |
||
| 1231 | end; |
||
| 1232 | end; |
||
| 1233 | |||
| 1234 | |||
| 1235 | hi := 1023; |
||
| 1236 | lo := 0; |
||
| 1237 | mid := 511; |
||
| 1238 | |||
| 1239 | while hi > lo do |
||
| 1240 | begin |
||
| 1241 | if Cos(mid / 2048.0 * Pi) > v.x then |
||
| 1242 | lo := mid + 1 |
||
| 1243 | else |
||
| 1244 | hi := mid; |
||
| 1245 | mid := (hi + lo) shr 1; |
||
| 1246 | end; |
||
| 1247 | |||
| 1248 | case sg of |
||
| 1249 | 1: result := mid; |
||
| 1250 | 2: result := 2047 - mid; |
||
| 1251 | 3: result := 2048 + mid; |
||
| 1252 | 4: result := 4095 - mid; |
||
| 1253 | end; |
||
| 1254 | |||
| 1255 | // to radians |
||
| 1256 | Result := Result * Pi / 2048.0; |
||
| 1257 | end; |
||
| 1258 | |||
| 1259 | function D2DMath_VecRot(const a: TD2DVector; const angle: Double): TD2DVector; |
||
| 1260 | begin |
||
| 1261 | Result.X := a.X * Cos(angle) - a.Y * Sin(angle); |
||
| 1262 | Result.Y := a.X * Sin(angle) + a.Y * Cos(angle); |
||
| 1263 | end; |
||
| 1264 | |||
| 1265 | |||
| 1266 | function D2DMath_VecScale(const a: TD2DVector; const scale: Double): TD2DVector; |
||
| 1267 | begin |
||
| 1268 | Result.X := a.X * scale; |
||
| 1269 | Result.Y := a.Y * scale; |
||
| 1270 | end; |
||
| 1271 | |||
| 1272 | function D2DMath_VecChangeLength(const a: TD2DVector; const k: Single): TD2DVector; |
||
| 1273 | var |
||
| 1274 | len: Single; |
||
| 1275 | begin |
||
| 1276 | len := D2DMath_VecLength(a); |
||
| 1277 | if len = 0 then |
||
| 1278 | begin |
||
| 1279 | Result := MakeD2DVector(0, 0); |
||
| 1280 | Exit; |
||
| 1281 | end; |
||
| 1282 | |||
| 1283 | Result.X := a.X * k / len; |
||
| 1284 | Result.Y := a.Y * k / len; |
||
| 1285 | end; |
||
| 1286 | |||
| 1287 | function D2DMath_VecLookAt(const pos: TD2DVector; const target: TD2DVector; const k: Single): TD2DVector; |
||
| 1288 | var |
||
| 1289 | sub: TD2DVector; |
||
| 1290 | len: Single; |
||
| 1291 | begin |
||
| 1292 | sub := D2DMath_VecSub(target, pos); |
||
| 1293 | len := D2DMath_VecLength(sub); |
||
| 1294 | if len = 0 then |
||
| 1295 | begin |
||
| 1296 | Result := MakeD2DVector(0, 0); |
||
| 1297 | Exit; |
||
| 1298 | end; |
||
| 1299 | |||
| 1300 | Result.X := sub.X * k / len; |
||
| 1301 | Result.Y := sub.Y * k / len; |
||
| 1302 | end; |
||
| 1303 | |||
| 1304 | function D2DMath_VecRandom2D(const k: Single): TD2DVector; |
||
| 1305 | begin |
||
| 1306 | Result := D2DMath_VecChangeLength(MakeD2DVector(Random - 0.5, Random - 0.5), k); |
||
| 1307 | end; |
||
| 1308 | |||
| 1309 | function D2DMath_VecLerp(const a: TD2DVector; const b: TD2DVector; const rate: Single): TD2DVector; |
||
| 1310 | begin |
||
| 1311 | Result.x := rate * b.x + (1.0 - rate) * a.x; |
||
| 1312 | Result.y := rate * b.y + (1.0 - rate) * a.y; |
||
| 1313 | end; |
||
| 1314 | |||
| 1315 | |||
| 1316 | end. |
||
| 1317 |