Using comments within the code itself, can you provide an line by line explanation of the below JavaScript file? The file itself deals with WebGl and if that helps you. Please & thank you JavaScript File: function inverse2(m) { var a = mat2(); var d = det2(m); a[0][0] = m[1][1]/d; a[0][1] = -m[0][1]/d; a[1][0] = -m[1][0]/d; a[1][1] = m[0][0]/d; return a; } function inverse3(m) { var a = mat3(); var d = det3(m); var a00 = [ vec2(m[1][1], m[1][2]), vec2(m[2][1], m[2][2]) ]; var a01 = [ vec2(m[1][0], m[1][2]), vec2(m[2][0], m[2][2]) ]; var a02 = [ vec2(m[1][0], m[1][1]), vec2(m[2][0], m[2][1]) ]; var a10 = [ vec2(m[0][1], m[0][2]), vec2(m[2][1], m[2][2]) ]; var a11 = [ vec2(m[0][0], m[0][2]), vec2(m[2][0], m[2][2]) ]; var a12 = [ vec2(m[0][0], m[0][1]), vec2(m[2][0], m[2][1]) ]; var a20 = [ vec2(m[0][1], m[0][2]), vec2(m[1][1], m[1][2]) ]; var a21 = [ vec2(m[0][0], m[0][2]), vec2(m[1][0], m[1][2]) ]; var a22 = [ vec2(m[0][0], m[0][1]), vec2(m[1][0], m[1][1]) ]; a[0][0] = det2(a00)/d; a[0][1] = -det2(a10)/d; a[0][2] = det2(a20)/d; a[1][0] = -det2(a01)/d; a[1][1] = det2(a11)/d; a[1][2] = -det2(a21)/d; a[2][0] = det2(a02)/d; a[2][1] = -det2(a12)/d; a[2][2] = det2(a22)/d; return a; } function inverse4(m) { var a = mat4(); var d = det4(m); var a00 = [ vec3(m[1][1], m[1][2], m[1][3]), vec3(m[2][1], m[2][2], m[2][3]), vec3(m[3][1], m[3][2], m[3][3]) ]; var a01 = [ vec3(m[1][0], m[1][2], m[1][3]), vec3(m[2][0], m[2][2], m[2][3]), vec3(m[3][0], m[3][2], m[3][3]) ]; var a02 = [ vec3(m[1][0], m[1][1], m[1][3]), vec3(m[2][0], m[2][1], m[2][3]), vec3(m[3][0], m[3][1], m[3][3]) ]; var a03 = [ vec3(m[1][0], m[1][1], m[1][2]), vec3(m[2][0], m[2][1], m[2][2]), vec3(m[3][0], m[3][1], m[3][2]) ]; var a10 = [ vec3(m[0][1], m[0][2], m[0][3]), vec3(m[2][1], m[2][2], m[2][3]), vec3(m[3][1], m[3][2], m[3][3]) ]; var a11 = [ vec3(m[0][0], m[0][2], m[0][3]), vec3(m[2][0], m[2][2], m[2][3]), vec3(m[3][0], m[3][2], m[3][3]) ]; var a12 = [ vec3(m[0][0], m[0][1], m[0][3]), vec3(m[2][0], m[2][1], m[2][3]), vec3(m[3][0], m[3][1], m[3][3]) ]; var a13 = [ vec3(m[0][0], m[0][1], m[0][2]), vec3(m[2][0], m[2][1], m[2][2]), vec3(m[3][0], m[3][1], m[3][2]) ]; var a20 = [ vec3(m[0][1], m[0][2], m[0][3]), vec3(m[1][1], m[1][2], m[1][3]), vec3(m[3][1], m[3][2], m[3][3]) ]; var a21 = [ vec3(m[0][0], m[0][2], m[0][3]), vec3(m[1][0], m[1][2], m[1][3]), vec3(m[3][0], m[3][2], m[3][3]) ]; var a22 = [ vec3(m[0][0], m[0][1], m[0][3]), vec3(m[1][0], m[1][1], m[1][3]), vec3(m[3][0], m[3][1], m[3][3]) ]; var a23 = [ vec3(m[0][0], m[0][1], m[0][2]), vec3(m[1][0], m[1][1], m[1][2]), vec3(m[3][0], m[3][1], m[3][2]) ]; var a30 = [ vec3(m[0][1], m[0][2], m[0][3]), vec3(m[1][1], m[1][2], m[1][3]), vec3(m[2][1], m[2][2], m[2][3]) ]; var a31 = [ vec3(m[0][0], m[0][2], m[0][3]), vec3(m[1][0], m[1][2], m[1][3]), vec3(m[2][0], m[2][2], m[2][3]) ]; var a32 = [ vec3(m[0][0], m[0][1], m[0][3]), vec3(m[1][0], m[1][1], m[1][3]), vec3(m[2][0], m[2][1], m[2][3]) ]; var a33 = [ vec3(m[0][0], m[0][1], m[0][2]), vec3(m[1][0], m[1][1], m[1][2]), vec3(m[2][0], m[2][1], m[2][2]) ]; a[0][0] = det3(a00)/d; a[0][1] = -det3(a10)/d; a[0][2] = det3(a20)/d; a[0][3] = -det3(a30)/d; a[1][0] = -det3(a01)/d; a[1][1] = det3(a11)/d; a[1][2] = -det3(a21)/d; a[1][3] = det3(a31)/d; a[2][0] = det3(a02)/d; a[2][1] = -det3(a12)/d; a[2][2] = det3(a22)/d; a[2][3] = -det3(a32)/d; a[3][0] = -det3(a03)/d; a[3][1] = det3(a13)/d; a[3][2] = -det3(a23)/d; a[3][3] = det3(a33)/d; return a; } function inverse(m) { if(!isMatrix(m)) throw("inverse: m not a matrix"); if(m.length == 2) return inverse2(m); if(m.length == 3) return inverse3(m); if(m.length == 4) return inverse4(m); } //--------------------------------------------------------- // normal matrix function normalMatrix(m, flag) { if(m.type!='mat4') throw "normalMatrix: input not a mat4"; var a = inverse(transpose(m)); if(arguments.length == 1 &&flag == false) return a; var b = mat3(); for(var i=0;i<3;i++) for(var j=0; j<3; j++) b[i][j] = a[i][j]; return b; }

Using comments within the code itself, can you provide an line by line explanation of the below JavaScript file? The file itself deals with WebGl and if that helps you. Please & thank you JavaScript File: function inverse2(m) { var a = mat2(); var d = det2(m); a[0][0] = m[1][1]/d; a[0][1] = -m[0][1]/d; a[1][0] = -m[1][0]/d; a[1][1] = m[0][0]/d; return a; } function inverse3(m) { var a = mat3(); var d = det3(m); var a00 = [ vec2(m[1][1], m[1][2]), vec2(m[2][1], m[2][2]) ]; var a01 = [ vec2(m[1][0], m[1][2]), vec2(m[2][0], m[2][2]) ]; var a02 = [ vec2(m[1][0], m[1][1]), vec2(m[2][0], m[2][1]) ]; var a10 = [ vec2(m[0][1], m[0][2]), vec2(m[2][1], m[2][2]) ]; var a11 = [ vec2(m[0][0], m[0][2]), vec2(m[2][0], m[2][2]) ]; var a12 = [ vec2(m[0][0], m[0][1]), vec2(m[2][0], m[2][1]) ]; var a20 = [ vec2(m[0][1], m[0][2]), vec2(m[1][1], m[1][2]) ]; var a21 = [ vec2(m[0][0], m[0][2]), vec2(m[1][0], m[1][2]) ]; var a22 = [ vec2(m[0][0], m[0][1]), vec2(m[1][0], m[1][1]) ]; a[0][0] = det2(a00)/d; a[0][1] = -det2(a10)/d; a[0][2] = det2(a20)/d; a[1][0] = -det2(a01)/d; a[1][1] = det2(a11)/d; a[1][2] = -det2(a21)/d; a[2][0] = det2(a02)/d; a[2][1] = -det2(a12)/d; a[2][2] = det2(a22)/d; return a; } function inverse4(m) { var a = mat4(); var d = det4(m); var a00 = [ vec3(m[1][1], m[1][2], m[1][3]), vec3(m[2][1], m[2][2], m[2][3]), vec3(m[3][1], m[3][2], m[3][3]) ]; var a01 = [ vec3(m[1][0], m[1][2], m[1][3]), vec3(m[2][0], m[2][2], m[2][3]), vec3(m[3][0], m[3][2], m[3][3]) ]; var a02 = [ vec3(m[1][0], m[1][1], m[1][3]), vec3(m[2][0], m[2][1], m[2][3]), vec3(m[3][0], m[3][1], m[3][3]) ]; var a03 = [ vec3(m[1][0], m[1][1], m[1][2]), vec3(m[2][0], m[2][1], m[2][2]), vec3(m[3][0], m[3][1], m[3][2]) ]; var a10 = [ vec3(m[0][1], m[0][2], m[0][3]), vec3(m[2][1], m[2][2], m[2][3]), vec3(m[3][1], m[3][2], m[3][3]) ]; var a11 = [ vec3(m[0][0], m[0][2], m[0][3]), vec3(m[2][0], m[2][2], m[2][3]), vec3(m[3][0], m[3][2], m[3][3]) ]; var a12 = [ vec3(m[0][0], m[0][1], m[0][3]), vec3(m[2][0], m[2][1], m[2][3]), vec3(m[3][0], m[3][1], m[3][3]) ]; var a13 = [ vec3(m[0][0], m[0][1], m[0][2]), vec3(m[2][0], m[2][1], m[2][2]), vec3(m[3][0], m[3][1], m[3][2]) ]; var a20 = [ vec3(m[0][1], m[0][2], m[0][3]), vec3(m[1][1], m[1][2], m[1][3]), vec3(m[3][1], m[3][2], m[3][3]) ]; var a21 = [ vec3(m[0][0], m[0][2], m[0][3]), vec3(m[1][0], m[1][2], m[1][3]), vec3(m[3][0], m[3][2], m[3][3]) ]; var a22 = [ vec3(m[0][0], m[0][1], m[0][3]), vec3(m[1][0], m[1][1], m[1][3]), vec3(m[3][0], m[3][1], m[3][3]) ]; var a23 = [ vec3(m[0][0], m[0][1], m[0][2]), vec3(m[1][0], m[1][1], m[1][2]), vec3(m[3][0], m[3][1], m[3][2]) ]; var a30 = [ vec3(m[0][1], m[0][2], m[0][3]), vec3(m[1][1], m[1][2], m[1][3]), vec3(m[2][1], m[2][2], m[2][3]) ]; var a31 = [ vec3(m[0][0], m[0][2], m[0][3]), vec3(m[1][0], m[1][2], m[1][3]), vec3(m[2][0], m[2][2], m[2][3]) ]; var a32 = [ vec3(m[0][0], m[0][1], m[0][3]), vec3(m[1][0], m[1][1], m[1][3]), vec3(m[2][0], m[2][1], m[2][3]) ]; var a33 = [ vec3(m[0][0], m[0][1], m[0][2]), vec3(m[1][0], m[1][1], m[1][2]), vec3(m[2][0], m[2][1], m[2][2]) ]; a[0][0] = det3(a00)/d; a[0][1] = -det3(a10)/d; a[0][2] = det3(a20)/d; a[0][3] = -det3(a30)/d; a[1][0] = -det3(a01)/d; a[1][1] = det3(a11)/d; a[1][2] = -det3(a21)/d; a[1][3] = det3(a31)/d; a[2][0] = det3(a02)/d; a[2][1] = -det3(a12)/d; a[2][2] = det3(a22)/d; a[2][3] = -det3(a32)/d; a[3][0] = -det3(a03)/d; a[3][1] = det3(a13)/d; a[3][2] = -det3(a23)/d; a[3][3] = det3(a33)/d; return a; } function inverse(m) { if(!isMatrix(m)) throw("inverse: m not a matrix"); if(m.length == 2) return inverse2(m); if(m.length == 3) return inverse3(m); if(m.length == 4) return inverse4(m); } //--------------------------------------------------------- // normal matrix function normalMatrix(m, flag) { if(m.type!='mat4') throw "normalMatrix: input not a mat4"; var a = inverse(transpose(m)); if(arguments.length == 1 &&flag == false) return a; var b = mat3(); for(var i=0;i<3;i++) for(var j=0; j<3; j++) b[i][j] = a[i][j]; return b; }

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

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Using comments within the code itself, can you provide an line by line explanation of the below JavaScript file? The file itself deals with WebGl and if that helps you.

Please & thank you

JavaScript File:

function inverse2(m)

{

var a = mat2();

var d = det2(m);

a[0][0] = m[1][1]/d;

a[0][1] = -m[0][1]/d;

a[1][0] = -m[1][0]/d;

a[1][1] = m[0][0]/d;

return a;

}

function inverse3(m)

{

var a = mat3();

var d = det3(m);

var a00 = [

vec2(m[1][1], m[1][2]),

vec2(m[2][1], m[2][2])

];

var a01 = [

vec2(m[1][0], m[1][2]),

vec2(m[2][0], m[2][2])

];

var a02 = [

vec2(m[1][0], m[1][1]),

vec2(m[2][0], m[2][1])

];

var a10 = [

vec2(m[0][1], m[0][2]),

vec2(m[2][1], m[2][2])

];

var a11 = [

vec2(m[0][0], m[0][2]),

vec2(m[2][0], m[2][2])

];

var a12 = [

vec2(m[0][0], m[0][1]),

vec2(m[2][0], m[2][1])

];

var a20 = [

vec2(m[0][1], m[0][2]),

vec2(m[1][1], m[1][2])

];

var a21 = [

vec2(m[0][0], m[0][2]),

vec2(m[1][0], m[1][2])

];

var a22 = [

vec2(m[0][0], m[0][1]),

vec2(m[1][0], m[1][1])

];

a[0][0] = det2(a00)/d;

a[0][1] = -det2(a10)/d;

a[0][2] = det2(a20)/d;

a[1][0] = -det2(a01)/d;

a[1][1] = det2(a11)/d;

a[1][2] = -det2(a21)/d;

a[2][0] = det2(a02)/d;

a[2][1] = -det2(a12)/d;

a[2][2] = det2(a22)/d;

return a;

}

function inverse4(m)

{

var a = mat4();

var d = det4(m);

var a00 = [

vec3(m[1][1], m[1][2], m[1][3]),

vec3(m[2][1], m[2][2], m[2][3]),

vec3(m[3][1], m[3][2], m[3][3])

];

var a01 = [

vec3(m[1][0], m[1][2], m[1][3]),

vec3(m[2][0], m[2][2], m[2][3]),

vec3(m[3][0], m[3][2], m[3][3])

];

var a02 = [

vec3(m[1][0], m[1][1], m[1][3]),

vec3(m[2][0], m[2][1], m[2][3]),

vec3(m[3][0], m[3][1], m[3][3])

];

var a03 = [

vec3(m[1][0], m[1][1], m[1][2]),

vec3(m[2][0], m[2][1], m[2][2]),

vec3(m[3][0], m[3][1], m[3][2])

];

var a10 = [

vec3(m[0][1], m[0][2], m[0][3]),

vec3(m[2][1], m[2][2], m[2][3]),

vec3(m[3][1], m[3][2], m[3][3])

];

var a11 = [

vec3(m[0][0], m[0][2], m[0][3]),

vec3(m[2][0], m[2][2], m[2][3]),

vec3(m[3][0], m[3][2], m[3][3])

];

var a12 = [

vec3(m[0][0], m[0][1], m[0][3]),

vec3(m[2][0], m[2][1], m[2][3]),

vec3(m[3][0], m[3][1], m[3][3])

];

var a13 = [

vec3(m[0][0], m[0][1], m[0][2]),

vec3(m[2][0], m[2][1], m[2][2]),

vec3(m[3][0], m[3][1], m[3][2])

];

var a20 = [

vec3(m[0][1], m[0][2], m[0][3]),

vec3(m[1][1], m[1][2], m[1][3]),

vec3(m[3][1], m[3][2], m[3][3])

];

var a21 = [

vec3(m[0][0], m[0][2], m[0][3]),

vec3(m[1][0], m[1][2], m[1][3]),

vec3(m[3][0], m[3][2], m[3][3])

];

var a22 = [

vec3(m[0][0], m[0][1], m[0][3]),

vec3(m[1][0], m[1][1], m[1][3]),

vec3(m[3][0], m[3][1], m[3][3])

];

var a23 = [

vec3(m[0][0], m[0][1], m[0][2]),

vec3(m[1][0], m[1][1], m[1][2]),

vec3(m[3][0], m[3][1], m[3][2])

];

var a30 = [

vec3(m[0][1], m[0][2], m[0][3]),

vec3(m[1][1], m[1][2], m[1][3]),

vec3(m[2][1], m[2][2], m[2][3])

];

var a31 = [

vec3(m[0][0], m[0][2], m[0][3]),

vec3(m[1][0], m[1][2], m[1][3]),

vec3(m[2][0], m[2][2], m[2][3])

];

var a32 = [

vec3(m[0][0], m[0][1], m[0][3]),

vec3(m[1][0], m[1][1], m[1][3]),

vec3(m[2][0], m[2][1], m[2][3])

];

var a33 = [

vec3(m[0][0], m[0][1], m[0][2]),

vec3(m[1][0], m[1][1], m[1][2]),

vec3(m[2][0], m[2][1], m[2][2])

];

a[0][0] = det3(a00)/d;

a[0][1] = -det3(a10)/d;

a[0][2] = det3(a20)/d;

a[0][3] = -det3(a30)/d;

a[1][0] = -det3(a01)/d;

a[1][1] = det3(a11)/d;

a[1][2] = -det3(a21)/d;

a[1][3] = det3(a31)/d;

a[2][0] = det3(a02)/d;

a[2][1] = -det3(a12)/d;

a[2][2] = det3(a22)/d;

a[2][3] = -det3(a32)/d;

a[3][0] = -det3(a03)/d;

a[3][1] = det3(a13)/d;

a[3][2] = -det3(a23)/d;

a[3][3] = det3(a33)/d;

return a;

}

function inverse(m)

{

if(!isMatrix(m)) throw("inverse: m not a matrix");

if(m.length == 2) return inverse2(m);

if(m.length == 3) return inverse3(m);

if(m.length == 4) return inverse4(m);

}

//---------------------------------------------------------

// normal matrix

function normalMatrix(m, flag)

{

if(m.type!='mat4') throw "normalMatrix: input not a mat4";

var a = inverse(transpose(m));

if(arguments.length == 1 &&flag == false) return a;

var b = mat3();

for(var i=0;i<3;i++) for(var j=0; j<3; j++) b[i][j] = a[i][j];

return b;

}

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