/* * All or portions of this file Copyright (c) Amazon.com, Inc. or its affiliates or * its licensors. * * For complete copyright and license terms please see the LICENSE at the root of this * distribution (the "License"). All use of this software is governed by the License, * or, if provided, by the license below or the license accompanying this file. Do not * remove or modify any license notices. This file is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * */ // include the required headers #include #include #include #include #include namespace MCore { // project a 3D point in world space to 2D screen coordinates AZ::Vector3 Project(const AZ::Vector3& point, const AZ::Matrix4x4& viewProjMatrix, uint32 screenWidth, uint32 screenHeight) { // 1. expand homogenous coordinate AZ::Vector4 expandedPoint(point.GetX(), point.GetY(), point.GetZ(), 1.0f); // 2. multiply by the view and the projection matrix (note that this is a four component matrix multiplication, so no affine one!) expandedPoint = viewProjMatrix * expandedPoint; // 3. perform perspective division for the x and y coordinates only expandedPoint.SetX(expandedPoint.GetX() / expandedPoint.GetW()); expandedPoint.SetY(expandedPoint.GetY() / expandedPoint.GetW()); // 4. map them to the screen space AZ::Vector3 result( (1.0f + expandedPoint.GetX()) * (float)screenWidth * 0.5f, (1.0f - expandedPoint.GetY()) * (float)screenHeight * 0.5f, // 5. get the distance to the camera lense plane expandedPoint.GetZ()); return result; } // unproject into eye space, remember this means the resulting vector will be in camera space already // drawing lines that take world space coordinates with those returned coordinates will apply a camera tranform twice AZ::Vector3 UnprojectToEyeSpace(float screenX, float screenY, const AZ::Matrix4x4& invProjMat, float windowWidth, float windowHeight, float depth) { // convert to normalized device coordinates in range of -1 to +1 const float x = 2.0f * (screenX / windowWidth) - 1.0f; const float y = 1.0f - 2.0f * (screenY / windowHeight); // convert into clip space AZ::Vector4 vec(x, y, 1, 0.0f); vec = invProjMat * vec; // return the result at the given desired depth return AZ::Vector3(vec.GetX(), vec.GetY(), vec.GetZ()).GetNormalized() * depth; } // unproject screen coordinates to a 3D point in world space AZ::Vector3 Unproject(float screenX, float screenY, float screenWidth, float screenHeight, float depth, const AZ::Matrix4x4& invProjMat, const AZ::Matrix4x4& invViewMat) { // convert to normalized device coordinates in range of -1 to +1 const float x = 2.0f * (screenX / screenWidth) - 1.0f; const float y = 1.0f - 2.0f * (screenY / screenHeight); // flip y // convert into clip space AZ::Vector4 vec(x, y, 1.0f, 0.0f); vec = invProjMat * vec; // return the result at the given desired depth and transform from eyespace into world space return invViewMat * (AZ::Vector3(vec.GetX(), vec.GetY(), vec.GetZ()).GetNormalized() * depth); } AZ::Vector3 UnprojectOrtho(float screenX, float screenY, float screenWidth, float screenHeight, float depth, const AZ::Matrix4x4& projectionMatrix, const AZ::Matrix4x4& viewMatrix) { // 1. normalize the screen coordinates so that it will be in range [-1.0, 1.0] const float normalizedX = 2.0f * (screenX / (float)screenWidth) - 1.0f; const float normalizedY = 2.0f * (screenY / (float)screenHeight) - 1.0f; // 2. expand homogenous coordinate AZ::Vector4 expandedPoint(normalizedX, -normalizedY, depth, 1.0f); // 3. multiply by the inverse of the projection matrix expandedPoint = MCore::InvertProjectionMatrix(projectionMatrix) * expandedPoint; // 4. multiply by the inverse of the modelview matrix expandedPoint = MCore::InvertProjectionMatrix(viewMatrix) * expandedPoint; // 5. perform perspective division expandedPoint /= expandedPoint.GetW(); //MCore::LogDebug("screenCoords: %i %i, unitCubeValues: (%.2f, %.2f, %.2f) result: (%.2f, %.2f, %.2f, %.2f)", screenX, screenY, normalizedX, normalizedY, normalizedDepth, expandedPoint.x, expandedPoint.y, expandedPoint.z, expandedPoint.w); // 6. project down to three components again return AZ::Vector3(expandedPoint.GetX(), expandedPoint.GetY(), expandedPoint.GetZ()); } // convert from cartesian coordinates into spherical coordinates // this uses the y-axis (up) and x-axis (right) as basis // the vector needs to be normalized! AZ::Vector2 ToSpherical(const AZ::Vector3& normalizedVector) { return AZ::Vector2(Math::ATan2(normalizedVector.GetY(), normalizedVector.GetX()), Math::ACos(normalizedVector.GetZ())); } // convert from spherical coordinates back into cartesian coordinates // this uses the y-axis (up) and x-axis (right) as basis AZ::Vector3 FromSpherical(const AZ::Vector2& spherical) { return AZ::Vector3( Math::Cos(spherical.GetX()), Math::Sin(spherical.GetX()) * Math::Sin(spherical.GetY()), Math::Sin(spherical.GetX()) * Math::Cos(spherical.GetY())); } // calculate sample rate info void CalcSampleRateInfo(float samplesPerSecond, float duration, float* outSampleTimeStep, uint32* outNumSamples) { if (samplesPerSecond < MCore::Math::epsilon) { samplesPerSecond = MCore::Math::epsilon; } float sampleTimeStep = 1.0f / samplesPerSecond; if (sampleTimeStep >= duration) { *outSampleTimeStep = duration; *outNumSamples = 2; return; } const uint32 numSamples = (uint32)(duration * samplesPerSecond) + 1; const float timeStepError = MCore::Math::FMod(duration, sampleTimeStep); const float beforeSampleTimeStep = sampleTimeStep; sampleTimeStep += (timeStepError / (float)(numSamples - 1)); if (sampleTimeStep * (numSamples - 1) > duration + MCore::Math::epsilon) { sampleTimeStep = beforeSampleTimeStep; } *outSampleTimeStep = sampleTimeStep; *outNumSamples = numSamples; } // calculate the area of the triangles made of the given three points double CalcTriangleAreaAccurate(const AZ::Vector3& v1, const AZ::Vector3& v2, const AZ::Vector3& v3) { // first point const double ax = v3.GetX() - v2.GetX(); const double ay = v3.GetY() - v2.GetY(); const double az = v3.GetZ() - v2.GetZ(); // second point const double bx = v1.GetX() - v3.GetX(); const double by = v1.GetY() - v3.GetY(); const double bz = v1.GetZ() - v3.GetZ(); // third point const double cx = v2.GetX() - v1.GetX(); const double cy = v2.GetY() - v1.GetY(); const double cz = v2.GetZ() - v1.GetZ(); // squared lengths of the triangle sides const double squaredA = ax * ax + ay * ay + az * az; const double squaredB = bx * bx + by * by + bz * bz; const double squaredC = cx * cx + cy * cy + cz * cz; // safety check if (squaredA == 0.0 || squaredB == 0.0 || squaredC == 0.0) { return 0.0; } // calculate the lengths of the triangle const double a = sqrt(squaredA); const double b = sqrt(squaredB); const double c = sqrt(squaredC); // heron's formula const double halfPerimeter = (a + b + c) / 2.0; const double squaredArea = halfPerimeter * (halfPerimeter - a) * (halfPerimeter - b) * (halfPerimeter - c); const double area = sqrt(squaredArea); // return the result return area; } // calculate the area of the triangles made of the given three points float CalcTriangleArea(const AZ::Vector3& v1, const AZ::Vector3& v2, const AZ::Vector3& v3) { // calculate the lengths of the triangle const float a = SafeLength(v3 - v2); const float b = SafeLength(v1 - v3); const float c = SafeLength(v2 - v1); // heron's formula const float halfPerimeter = (a + b + c) / 2.0f; const float squaredArea = halfPerimeter * (halfPerimeter - a) * (halfPerimeter - b) * (halfPerimeter - c); const float area = sqrt(squaredArea); // return the result return area; } // orthogonal projection on the xz plane AZ::Vector2 OrthogonalProject(const AZ::Vector3& pos) { return AZ::Vector2(pos.GetX(), pos.GetZ()); } // orthogonal unproject from the xz plane back onto the sphere AZ::Vector3 OrthogonalUnproject(const AZ::Vector2& uv) { AZ::Vector3 outDirection; outDirection.SetX(uv.GetX()); outDirection.SetZ(uv.GetY()); outDirection.SetY(Math::SafeSqrt(-(outDirection.GetX() * outDirection.GetX()) - (outDirection.GetZ() * outDirection.GetZ()) + 1.0f)); // find the right height on the sphere for this ortho xy coord return SafeNormalize(outDirection); } // stereographic project AZ::Vector2 StereographicProject(const AZ::Vector3& pos) { AZ::Vector2 result; const float div = (1.0f - pos.GetY()) + Math::epsilon; result.SetX(pos.GetX() / div); result.SetY(pos.GetZ() / div); return result; } // stereographic unproject AZ::Vector3 StereographicUnproject(const AZ::Vector2& uv) { AZ::Vector3 result; const float s = 2.0f / (uv.GetX() * uv.GetX() + uv.GetY() * uv.GetY() + 1.0f); result.SetX(s * uv.GetX()); result.SetY(1.0f - s); result.SetZ(s * uv.GetY()); return result; } // check if a given point is inside a 2d convex/concave polygon // it does this by checking how many times a line intersects with the poly (how many times it goes inside and outside again) bool PointInPoly(AZ::Vector2* verts, uint32 numVerts, const AZ::Vector2& point) { uint32 c = 0; for (uint32 i = 0, j = numVerts - 1; i < numVerts; j = i++) { if (((verts[i].GetY() > point.GetY()) != (verts[j].GetY() > point.GetY())) && (point.GetX() < (verts[j].GetX() - verts[i].GetX()) * (point.GetY() - verts[i].GetY()) / (verts[j].GetY() - verts[i].GetY()) + verts[i].GetX())) { c = !c; } } return (c > 0); } // get the distance to a given edge float DistanceToEdge(const AZ::Vector2& edgePointA, const AZ::Vector2& edgePointB, const AZ::Vector2& testPoint) { // Return minimum distance between line segment vw and point p AZ::Vector2 edgeVector = edgePointB - edgePointA; const float l2 = edgeVector.GetLengthSq(); if (l2 < Math::epsilon) { return (testPoint - edgePointA).GetLength(); } // Consider the line extending the segment, parameterized as v + t (w - v). // We find projection of point p onto the line. // It falls where t = [(p-v) . (w-v)] / |w-v|^2 // We clamp t from [0,1] to handle points outside the segment vw. const float dot = (testPoint - edgePointA).Dot(edgeVector); const float t = Max(0.0f, Min(1.0f, dot / l2)); const AZ::Vector2 projection = edgePointA + t * edgeVector; // Projection falls on the segment return (testPoint - projection).GetLength(); } // check if the test point is inside the polygon AZ::Vector2 ClosestPointToPoly(const AZ::Vector2* polyPoints, uint32 numPoints, const AZ::Vector2& testPoint) { AZ::Vector2 result; float closestDist = FLT_MAX; for (uint32 i = 0; i < numPoints; ++i) { AZ::Vector2 edgePointA; AZ::Vector2 edgePointB; if (i < numPoints - 1) { edgePointA = polyPoints[i]; edgePointB = polyPoints[i + 1]; } else { edgePointA = polyPoints[i]; edgePointB = polyPoints[0]; } float dist; AZ::Vector2 projection; AZ::Vector2 edgeVector = edgePointB - edgePointA; const float l2 = edgeVector.GetLengthSq(); if (l2 < Math::epsilon) { dist = (testPoint - edgePointA).GetLength(); projection = edgePointA; } else { const float dot = (testPoint - edgePointA).Dot(edgeVector); const float t = Max(0.0f, Min(1.0f, dot / l2)); projection = edgePointA + t * edgeVector; dist = (testPoint - projection).GetLength(); } if (dist < closestDist) { closestDist = dist; result = projection; } } return result; } // static CRC lookup table /*static uint32 CRC32Table[256] = { 0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA, 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3, 0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988, 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91, 0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE, 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7, 0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC, 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5, 0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172, 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B, 0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940, 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59, 0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116, 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F, 0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924, 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D, 0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A, 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433, 0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818, 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01, 0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E, 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457, 0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C, 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65, 0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2, 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB, 0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0, 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9, 0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086, 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F, 0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4, 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD, 0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A, 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683, 0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8, 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1, 0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE, 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7, 0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC, 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5, 0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252, 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B, 0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60, 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79, 0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236, 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F, 0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04, 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D, 0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A, 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713, 0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38, 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21, 0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E, 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777, 0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C, 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45, 0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2, 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB, 0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0, 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9, 0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6, 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF, 0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94, 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D, }; // calculate the CRC32 void CalcCRC32(uint8 byteValue, uint32& CRC) { CRC = ((CRC) >> 8) ^ MCore::CRC32Table[(byteValue) ^ ((CRC) & 0x000000FF)]; }*/ } // namespace MCore