{"id":522,"date":"2021-12-05T20:05:01","date_gmt":"2021-12-05T20:05:01","guid":{"rendered":"https:\/\/writingagame.com\/?p=522"},"modified":"2023-05-15T20:52:04","modified_gmt":"2023-05-15T20:52:04","slug":"chapter-14-3d-coordinates-and-game-subjects","status":"publish","type":"post","link":"https:\/\/writingagame.com\/index.php\/2021\/12\/05\/chapter-14-3d-coordinates-and-game-subjects\/","title":{"rendered":"Chapter 14. 3D Coordinates and Game Subjects"},"content":{"rendered":"\n

3D subject will require 3D coordinates including orientation angles. We will need Euler angles (yaw, pitch, and roll in aviation terminology or heading, attitude and bank in naval). We’ll start with Euler angles in degrees and in radians and a rotation Matrix<\/em>. We’ll call this class Coords<\/strong>.<\/p>\n\n\n\n

Windows<\/h2>\n\n\n\n

1. Start VS. Open C:\\CPP\\a998engine\\p_windows\\p_windows.sln<\/em>.<\/p>\n\n\n\n

\n\n\n\n

2. Under xEngine <\/em>add new header file Coords.h<\/strong><\/p>\n\n\n\n

Location: C:\\CPP\\engine<\/em><\/p>\n\n\n\n

Code:<\/p>\n\n\n

\n#pragma once\n#include "linmath.h"\n\nclass Coords\n{\nprivate:\n\tfloat eulerDg[3] = { 0,0,0 }; \/\/Euler angles (yaw, pitch, and roll) in degrees\n\tfloat eulerRd[3] = { 0,0,0 }; \/\/Euler angles in radians\n\tmat4x4 rotationMatrix = { 1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1 };\n\t\/\/mat4x4 rotationMatrix = { {1,0,0,0}, {0,1,0,0}, {0,0,1,0}, {0,0,0,1} };\npublic:\n\tfloat pos[4] = { 0,0,0,0 }; \/\/x,y,z position + 4-th element for compatibility with 3D 4x4 matrices math\npublic:\n\tvoid setDegrees(float ax, float ay, float az) { setDegrees(this, ax, ay, az); };\n\tstatic void setDegrees(Coords* pC, float ax, float ay, float az);\n\tfloat getRd(int i) { return eulerRd[i]; }; \/\/get angle in radians\n\t\/\/float getDg(int i) { return eulerDg[i]; }; \/\/get angle in degrees\n\tvoid setPosition(float kx, float ky, float kz) { setPosition(this, kx, ky, kz); };\n\tstatic void setPosition(Coords* pC, float kx, float ky, float kz);\n\tmat4x4* getRotationMatrix() { return &rotationMatrix; };\n\tvoid setRotationMatrix(mat4x4 m) { setRotationMatrix(this, m); };\n\tstatic void setRotationMatrix(Coords* pC, mat4x4 m);\n\tstatic void eulerRdToMatrix(mat4x4 rotationMatrix, float* eulerRd);\n\tstatic void matrixToEulerRd(float* eulerRd, mat4x4 m);\n};\n\n<\/pre><\/div>\n\n\n
<\/p>\n\n\n\n
\n\n\n\n
3. Under xEngine <\/em>add new C++ file Coords.cpp<\/strong><\/p>\n\n\n\n
Location: C:\\CPP\\engine<\/em><\/p>\n\n\n\n
Code:<\/p>\n\n\n
\n#include "Coords.h"\n#include "platform.h"\n#include <string>\n\nfloat PI = 3.141592f;\nfloat degrees2radians = PI \/ 180.0f;\nfloat radians2degrees = 180.0f \/ PI;\n\nvoid Coords::setDegrees(Coords* pC, float ax, float ay, float az) {\n\tif (pC->eulerDg[0] == ax && pC->eulerDg[1] == ay && pC->eulerDg[2] == az)\n\t\treturn;\n\tpC->eulerDg[0] = ax;\n\tpC->eulerDg[1] = ay;\n\tpC->eulerDg[2] = az;\n\t\/\/convert to radians\n\tpC->eulerRd[0] = pC->eulerDg[0] * degrees2radians;\n\tpC->eulerRd[1] = pC->eulerDg[1] * degrees2radians;\n\tpC->eulerRd[2] = pC->eulerDg[2] * degrees2radians;\n\t\/\/re-build rotation matrix\n\teulerRdToMatrix(pC->rotationMatrix, pC->eulerRd);\n}\nvoid Coords::eulerRdToMatrix(mat4x4 rotationMatrix, float* eulerRd){\n\t\/\/builds rotation matrix from Euler angles (in radians)\n\tmat4x4_identity(rotationMatrix);\n\t\/\/rotation order: Z-X-Y\n\tfloat a = eulerRd[1];\n\tif (a != 0)\n\t\tmat4x4_rotate_Y(rotationMatrix, rotationMatrix, a);\n\ta = eulerRd[0];\n\tif (a != 0)\n\t\tmat4x4_rotate_X(rotationMatrix, rotationMatrix, a);\n\ta = eulerRd[2];\n\tif (a != 0)\n\t\tmat4x4_rotate_Z(rotationMatrix, rotationMatrix, a);\n}\nvoid Coords::setPosition(Coords* pC, float kx, float ky, float kz) {\n\tpC->pos[0] = kx;\n\tpC->pos[1] = ky;\n\tpC->pos[2] = kz;\n}\nvoid Coords::setRotationMatrix(Coords* pC, mat4x4 m) {\n\tmemcpy(pC->rotationMatrix, m, sizeof(pC->rotationMatrix));\n\t\/\/update Euler angles\n\tmatrixToEulerRd(pC->eulerRd, pC->rotationMatrix);\n\n\tpC->eulerDg[0] = pC->eulerRd[0] * radians2degrees;\n\tpC->eulerDg[1] = pC->eulerRd[1] * radians2degrees;\n\tpC->eulerDg[2] = pC->eulerRd[2] * radians2degrees;\n}\nvoid Coords::matrixToEulerRd(float* eulerRd, mat4x4 m) {\n\t\/\/calculates Euler angles (in radians) from matrix\n\tfloat yaw, pitch, roll;\n\n\tif (m[1][2] > 0.998 || m[1][2] < -0.998) { \/\/ singularity at south or north pole\n\t\tyaw = atan2f(-m[2][0], m[0][0]);\n\t\troll = 0;\n\t}\n\telse {\n\t\tyaw = atan2f(-m[0][2], m[2][2]);\n\t\troll = atan2f(-m[1][0], m[1][1]);\n\t}\n\tpitch = asinf(m[1][2]);\n\n\teulerRd[0] = pitch;\n\teulerRd[1] = yaw;\n\teulerRd[2] = roll;\n}\n\n<\/pre><\/div>\n\n\n
<\/p>\n\n\n\n
\n\n\n\n
GameSubj <\/strong>class for beginning will include coordinates, speed (at this point we’re mostly interested in rotation speed), modelMatrix <\/em>for rendering, and a reference to involved DrawJobs <\/em>(it’s 2 variables: djStartN <\/em>and djTotalN<\/em>)<\/p>\n\n\n\n
4. Under xEngine <\/em>add new header file GameSubj.h<\/strong><\/p>\n\n\n\n
Location: C:\\CPP\\engine<\/em><\/p>\n\n\n\n
Code:<\/p>\n\n\n
\n#pragma once\n#include "Coords.h"\n#include "Material.h"\n#include <string>\n\nclass GameSubj\n{\npublic:\n\tstd::string name;\n\tCoords ownCoords;\n\tCoords ownSpeed;\n\tfloat scale[3] = { 1,1,1 };\n\tint djStartN = 0; \/\/first DJ N in DJs array (DrawJob::drawJobs)\n\tint djTotalN = 0; \/\/number of DJs\n\tmat4x4 ownModelMatrix = { 1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1 };\n\n\tMaterial* pAltMaterial = NULL;\n\npublic:\n\tvirtual ~GameSubj();\n\tvoid buildModelMatrix() { buildModelMatrix(this); };\n\tstatic void buildModelMatrix(GameSubj* pGS);\n\tvirtual int moveSubj() { return moveSubj(this); };\n\tstatic int moveSubj(GameSubj* pGS);\n};\n\n<\/pre><\/div>\n\n\n
<\/p>\n\n\n\n
\n\n\n\n
5. Under xEngine <\/em>add new C++ file GameSubj.cpp<\/strong><\/p>\n\n\n\n
Location: C:\\CPP\\engine<\/em><\/p>\n\n\n\n
Code:<\/p>\n\n\n
\n#include "GameSubj.h"\n#include "platform.h"\n\nGameSubj::~GameSubj() {\n    if (pAltMaterial != NULL)\n        delete pAltMaterial;\n}\nvoid GameSubj::buildModelMatrix(GameSubj* pGS) {\n    mat4x4_translate(pGS->ownModelMatrix, pGS->ownCoords.pos[0], pGS->ownCoords.pos[1], pGS->ownCoords.pos[2]);\n    \/\/rotation order: Z-X-Y\n    mat4x4_mul(pGS->ownModelMatrix, pGS->ownModelMatrix, *(pGS->ownCoords.getRotationMatrix()));\n\n    if (pGS->scale[0] != 1 || pGS->scale[1] != 1 || pGS->scale[2] != 1)\n        mat4x4_scale_aniso(pGS->ownModelMatrix, pGS->ownModelMatrix, pGS->scale[0], pGS->scale[1], pGS->scale[2]);\n}\nint GameSubj::moveSubj(GameSubj* pGS) {\n    if (pGS->ownSpeed.getRd(0) != 0 || pGS->ownSpeed.getRd(1) != 0 || pGS->ownSpeed.getRd(2) != 0) {\n        \/\/apply angle speed\n        mat4x4 newRotationMatrix;\n        mat4x4_mul(newRotationMatrix, *(pGS->ownCoords.getRotationMatrix()), *(pGS->ownSpeed.getRotationMatrix()));\n        pGS->ownCoords.setRotationMatrix(newRotationMatrix);\n    }\n    return 1;\n}\n\n<\/pre><\/div>\n\n\n
<\/p>\n\n\n\n
We have 2 functions here so far:<\/p>\n\n\n\n
buildModelMatrix()<\/em> which builds ownModelMatrix <\/em>for rendering from given coordinates and
moveSubj()<\/em> which at this point applies rotation speed to model’s coordinates (in matrix form) and forces to recalculate model’s Euler angles from resulting matrix by calling setRotationMatrix()<\/em> and matrixToEulerRd()<\/em> functions.<\/p>\n\n\n\n
\n\n\n\n
In TheGame.h<\/em> we’ll need an array (vector) of 3D gameSubjs. <\/p>\n\n\n\n
6. So, replace TheGame.h<\/em> code by:<\/p>\n\n\n
\n#pragma once\n#include <vector>\n#include "GameSubj.h"\n\nclass TheGame\n{\npublic:\n\tint screenSize[2];\n\tfloat screenRatio;\n\tbool bExitGame;\n\n\t\/\/static arrays (vectors) of active GameSubjs\n\tstatic std::vector<GameSubj*> gameSubjs;\npublic:\n\tint run();\n\tint getReady();\n\tint drawFrame();\n\tint cleanUp();\n\tint onScreenResize(int width, int height);\n};\n\n<\/pre><\/div>\n\n\n
<\/p>\n\n\n\n
\n\n\n\n
In TheGame.cpp<\/em> we will use our textured rectangle as a simple 3D model. The command glEnable(GL_CULL_FACE)<\/em> will instruct OpenGL to render only side, that facing us and to ignore another one. OpenGL considers surface “facing us” if vertices are going in counter-clockwise order.<\/p>\n\n\n\n
In the getReady()<\/em> function we will create a GameSubj<\/em>, a VBO <\/em>and corresponding DrawJob<\/em>.<\/p>\n\n\n\n
In the drawFrame()<\/em> we will scan gameSubjs <\/em>array (consisting of 1 subject), for each (only 1 at this point) subject we’ll call pGS->moveSubj()<\/em> function which will apply rotation speed to angle coordinates, then it will build MVP matrix and execute involved DrawJobs<\/em>.<\/p>\n\n\n\n
7. Open  TheGame.cpp<\/em>  and replace code by:<\/p>\n\n\n
\n#include "TheGame.h"\n#include "platform.h"\n#include "linmath.h"\n#include "Texture.h"\n#include "Shader.h"\n#include "DrawJob.h"\n\nextern std::string filesRoot;\n\n\/\/static array (vector) for loaded gameSubjs\nstd::vector<GameSubj*> TheGame::gameSubjs;\n\nstatic const struct\n{\n    float x, y, z, tu, tv;\n} frontVertices[4] =\n{\n    { -0.5f,  0.5f, 0.f, 0.f, 0.f }, \/\/top-left\n    { -0.5f, -0.5f, 0.f, 0.f, 1.f }, \/\/bottom-left\n    {  0.5f,  0.5f, 0.f, 1.f, 0.f }, \/\/top-right\n    {  0.5f, -0.5f, 0.f, 1.f, 1.f }  \/\/bottom-right\n};\n\nint TheGame::getReady() {\n    bExitGame = false;\n    Shader::loadShaders();\n    glEnable(GL_CULL_FACE);\n\n    GameSubj* pGS = new GameSubj();\n    gameSubjs.push_back(pGS);\n    pGS->djStartN = DrawJob::drawJobs.size();\n\n    pGS->name.assign("img1");\n    \/\/pGS->ownCoords.setPosition(-50, 50, 0);\n    pGS->ownSpeed.setDegrees(1, 2, 3);\n    pGS->scale[0] = 400;\n    pGS->scale[1] = pGS->scale[0] \/ 2;\n\n    \/\/face DrawJob\n    \/\/build VBO\n    unsigned int VBOid = DrawJob::newBufferId();\n    glBindBuffer(GL_ARRAY_BUFFER, VBOid);\n    glBufferData(GL_ARRAY_BUFFER, sizeof(frontVertices), frontVertices, GL_STATIC_DRAW);\n    int stride = sizeof(float) * 5;\n    \/\/add DrawJob\n    DrawJob* pDJ = new DrawJob();\n    pDJ->pointsN = 4; \/\/number of vertices\n    \/\/define material\n    pDJ->mt.shaderN = Shader::spN_flat_tex;\n    pDJ->mt.primitiveType = GL_TRIANGLE_STRIP;\n    pDJ->mt.uTex0 = Texture::loadTexture(filesRoot + "\/dt\/sample_img.png");\n    \/\/attributes references\n    AttribRef* pAR;\n    pAR = &pDJ->aPos; pAR->offset = 0;                 pAR->glVBOid = VBOid; pAR->stride = stride;\n    pAR = &pDJ->aTuv; pAR->offset = sizeof(float) * 3; pAR->glVBOid = VBOid; pAR->stride = stride;\n    \/\/create and fill vertex attributes array (VAO)\n    pDJ->buildVAO();\n    pGS->djTotalN = DrawJob::drawJobs.size() - pGS->djStartN;\n\n    return 1;\n}\nint TheGame::drawFrame() {\n    myPollEvents();\n\n    \/\/glClearColor(0.0, 0.0, 0.5, 1.0);\n    glClear(GL_COLOR_BUFFER_BIT);\n    mat4x4 mProjection, mMVP;\n    mat4x4_ortho(mProjection, -(float)screenSize[0] \/ 2, (float)screenSize[0] \/ 2, -(float)screenSize[1] \/ 2, (float)screenSize[1] \/ 2, 200.f, -200.f);\n\n    \/\/scan subjects\n    int subjsN = gameSubjs.size();\n    for (int subjN = 0; subjN < subjsN; subjN++) {\n        GameSubj* pGS = gameSubjs.at(subjN);\n        \/\/behavior - apply rotation speed\n        pGS->moveSubj();\n        \/\/prepare subject for rendering\n        pGS->buildModelMatrix(pGS);\n        \/\/build MVP matrix for given subject\n        mat4x4_mul(mMVP, mProjection, pGS->ownModelMatrix);\n        \/\/render subject\n        for (int i = 0; i < pGS->djTotalN; i++) {\n            DrawJob* pDJ = DrawJob::drawJobs.at(pGS->djStartN + i);\n            pDJ->execute((float*)mMVP, NULL);\n        }\n    }\n    mySwapBuffers();\n    return 1;\n}\nint TheGame::cleanUp() {\n    Texture::cleanUp();\n    Shader::cleanUp();\n    DrawJob::cleanUp();\n    return 1;\n}\nint TheGame::onScreenResize(int width, int height) {\n    if (screenSize[0] == width && screenSize[1] == height)\n        return 0;\n    screenSize[0] = width;\n    screenSize[1] = height;\n    screenRatio = (float)width \/ (float)height;\n    glViewport(0, 0, width, height);\n    mylog(" screen size %d x %d\\n", width, height);\n    return 1;\n}\nint TheGame::run() {\n    getReady();\n    while (!bExitGame) {\n        drawFrame();\n    }\n    cleanUp();\n    return 1;\n}\n\n<\/pre><\/div>\n\n\n
<\/p>\n\n\n\n
\n\n\n\n
8. Build and run:<\/p>\n\n\n\n
The image is spinning smoothly in all 3 dimensions, so our 3D functions are working properly.<\/p>\n\n\n\n
\n\n\n\n
Quaternions<\/strong>
Although they are in vogue lately, I still don’t see where they can replace matrices, even in complex 3D calculations involving all 3 axes. Just an alternative way to represent 3D rotation. Or am I missing something? Please correct me if I am wrong.<\/p>\n\n\n\n
    \n
  • Clarification: Eventually I did find them quite handy and rewrote this class accordingly.<\/li>\n<\/ul>\n\n\n\n
    <\/p>\n\n\n\n
    \n\n\n\n
    Android<\/h2>\n\n\n\n
    9. Re-start VS. Open C:\\CPP\\a998engine\\p_android\\p_android.sln<\/em>.<\/p>\n\n\n\n
    Under xEngine <\/em>add Existing Item,<\/p>\n\n\n\n
    Go to C:\\CPP\\engine<\/em>,<\/p>\n\n\n\n
    Pick<\/p>\n\n\n\n
      \n
    • Coords.cpp<\/li>\n\n\n\n
    • Coords.h<\/li>\n\n\n\n
    • GameSubj.cpp<\/li>\n\n\n\n
    • GameSubj.h<\/li>\n<\/ul>\n\n\n\n
      Add<\/strong><\/p>\n\n\n\n
      \n\n\n\n

      10. Switch on, unlock, plug in Android, allow.<\/p>\n\n\n\n
      Build and run. Cool.<\/p>\n\n\n\n
      \n\n\n\n
      <\/p>\n\n\n\n
      <\/p>\n","protected":false},"excerpt":{"rendered":"
      3D subject will require 3D coordinates including orientation angles. We will need Euler angles (yaw, pitch, and roll in aviation terminology or heading, attitude and bank in naval). We’ll start with Euler angles in degrees and in radians and a rotation Matrix. We’ll call this class Coords. Windows 1. Start VS. Open C:\\CPP\\a998engine\\p_windows\\p_windows.sln. 2. Under […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-522","post","type-post","status-publish","format-standard","hentry","category-cross-platform-3d"],"_links":{"self":[{"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/posts\/522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/comments?post=522"}],"version-history":[{"count":14,"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/posts\/522\/revisions"}],"predecessor-version":[{"id":1957,"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/posts\/522\/revisions\/1957"}],"wp:attachment":[{"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/media?parent=522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/categories?post=522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/writingagame.com\/index.php\/wp-json\/wp\/v2\/tags?post=522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}