opengl - GLSL聚光灯投影体积

Question

在我的开源项目中，我使用 Qt3D 设置了延迟渲染管道。到目前为止一切顺利，但现在我想通过添加聚光灯投影量来继续前进。（例如，好像场景中有烟雾） 像这样：

我正在使用的片段着色器位于问题的末尾。我已经读过，对于每个片段，我应该从灯光位置进行光线行进并找到与锥体的交叉点，但我不知道如何将其转换为 GLSL。我可以轻松地使用来自 GBuffer 的深度图（从相机的角度）添加制服，但我不知道这是否有帮助。

由于我的 GLSL 知识非常有限，请回复实际代码，而不是冗长的数学解释，我将无法理解/翻译成代码。请耐心等待我。

uniform sampler2D color;
uniform sampler2D position;
uniform sampler2D normal;
uniform vec2 winSize;

out vec4 fragColor;

const int MAX_LIGHTS = 102;
const int TYPE_POINT = 0;
const int TYPE_DIRECTIONAL = 1;
const int TYPE_SPOT = 2;

struct Light {
    int   type;
    vec3  position;
    vec3  color;
    float intensity;
    vec3  direction;
    float constantAttenuation;
    float linearAttenuation;
    float quadraticAttenuation;
    float cutOffAngle;
};

uniform Light lightsArray[MAX_LIGHTS];
uniform int lightsNumber;

void main()
{
    vec2 texCoord = gl_FragCoord.xy / winSize;
    vec4 col = texture(color, texCoord);
    vec3 pos = texture(position, texCoord).xyz;
    vec3 norm = texture(normal, texCoord).xyz;

    vec3 lightColor = vec3(0.0);
    vec3 s;
    float att;

    for (int i = 0; i < lightsNumber; ++i) {
        att = 1.0;
        if ( lightsArray[i].type != TYPE_DIRECTIONAL ) {
            s = lightsArray[i].position - pos;
            if (lightsArray[i].constantAttenuation != 0.0
             || lightsArray[i].linearAttenuation != 0.0
             || lightsArray[i].quadraticAttenuation != 0.0) {
                float dist = length(s);
                att = 1.0 / (lightsArray[i].constantAttenuation + lightsArray[i].linearAttenuation * dist + lightsArray[i].quadraticAttenuation * dist * dist);
            }
            s = normalize( s );
            if ( lightsArray[i].type == TYPE_SPOT ) {
                if ( degrees(acos(dot(-s, normalize(lightsArray[i].direction))) ) > lightsArray[i].cutOffAngle)
                    att = 0.0;
            }
        } else {
            s = normalize(-lightsArray[i].direction);
        }

        float diffuse = max( dot( s, norm ), 0.0 );

        lightColor += att * lightsArray[i].intensity * diffuse * lightsArray[i].color;
    }
    fragColor = vec4(col.rgb * lightColor, col.a);
}

这是使用上面的原始着色器时聚光灯的样子：

[编辑 - 已解决] 感谢 Rabbid76 出色的回答和宝贵的支持

这是查看圆锥投影的修改代码：

#version 140

uniform sampler2D color;
uniform sampler2D position;
uniform sampler2D normal;
uniform vec2 winSize;

out vec4 fragColor;

const int MAX_LIGHTS = 102;
const int TYPE_POINT = 0;
const int TYPE_DIRECTIONAL = 1;
const int TYPE_SPOT = 2;

struct Light {
    int type;
    vec3 position;
    vec3 color;
    float intensity;
    vec3 direction;
    float constantAttenuation;
    float linearAttenuation;
    float quadraticAttenuation;
    float cutOffAngle;
};

uniform Light lightsArray[MAX_LIGHTS];
uniform int lightsNumber;

uniform mat4 inverseViewMatrix; // defined by camera position, camera target and up vector

void main()
{
    vec2 texCoord = gl_FragCoord.xy / winSize;
    vec4 col = texture(color, texCoord);
    vec3 pos = texture(position, texCoord).xyz;
    vec3 norm = texture(normal, texCoord).xyz;

    vec3 lightColor = vec3(0.0);
    vec3 s;

    // calculate unprojected fragment position on near plane and line of sight relative to view
    float nearZ  = -1.0;
    vec3 nearPos = vec3( (texCoord.x - 0.5) * winSize.x / winSize.y, texCoord.y - 0.5, nearZ ); // 1.0 is camera near
    vec3 los     = normalize( nearPos );

    // ray definition
    vec3 O = vec3( inverseViewMatrix * vec4( 0.0, 0.0, 0.0, 1.0 ) ); // translation part of the camera matrix, which is equal to the camera position
    vec3 D = (length(pos) > 0.0) ? normalize(pos - O) : (mat3(inverseViewMatrix) * los);

    for (int i = 0; i < lightsNumber; ++i)
    {
        float att = 1.0;
        if ( lightsArray[i].type == TYPE_DIRECTIONAL )
        {
            s = normalize( -lightsArray[i].direction );
        }
        else
        {
            s = lightsArray[i].position - pos;

            if (lightsArray[i].type != TYPE_SPOT
                && (lightsArray[i].constantAttenuation != 0.0
                || lightsArray[i].linearAttenuation != 0.0
                || lightsArray[i].quadraticAttenuation != 0.0))
            {
                float dist = length(s);
                att = 1.0 / (lightsArray[i].constantAttenuation + lightsArray[i].linearAttenuation * dist + lightsArray[i].quadraticAttenuation * dist * dist);
            }

            s = normalize( s );
            if ( lightsArray[i].type == TYPE_SPOT )
            {

                // cone definition
                vec3  C     = lightsArray[i].position;
                vec3  V     = normalize(lightsArray[i].direction);
                float cosTh = cos( radians(lightsArray[i].cutOffAngle) );

                // ray - cone intersection
                vec3  CO     = O - C;
                float DdotV  = dot( D, V );
                float COdotV = dot( CO, V );
                float a      = DdotV * DdotV - cosTh * cosTh;
                float b      = 2.0 * (DdotV * COdotV - dot( D, CO ) * cosTh * cosTh);
                float c      = COdotV * COdotV - dot( CO, CO ) * cosTh * cosTh;
                float det    = b * b - 4.0 * a * c;

                // find intersection
                float isIsect = 0.0;
                vec3  isectP  = vec3(0.0);
                if ( det >= 0.0 )
                {
                    vec3  P1 = O + (-b - sqrt(det)) / (2.0 * a) * D;
                    vec3  P2 = O + (-b + sqrt(det)) / (2.0 * a) * D;
                    float isect1 = step( 0.0, dot(normalize(P1 - C), V) );
                    float isect2 = step( 0.0, dot(normalize(P2 - C), V) );
                    if ( isect1 < 0.5 )
                    {
                        P1 = P2;
                        isect1 = isect2;
                    }
                    if ( isect2 < 0.5 )
                    {
                        P2 = P1;
                        isect2 = isect1;
                    }
                    isectP = (length(P1 - O) < length(P2 - O)) ? P1 : P2;
                    isIsect = mix( isect2, 1.0, isect1 );

                    if ( length(pos) != 0.0 && length(isectP - O) > length(pos - O))
                        isIsect = 0.0;
                }

                float dist = length( isectP - C.xyz );
                float limit = degrees(acos(dot(-s, normalize(lightsArray[i].direction))) );

                if (isIsect > 0 || limit <= lightsArray[i].cutOffAngle)
                {
                    att  = 1.0 / dot( vec3( 1.0, dist, dist * dist ),
                                      vec3(lightsArray[i].constantAttenuation,
                                           lightsArray[i].linearAttenuation,
                                           lightsArray[i].quadraticAttenuation) );
                }
                else
                    att = 0.0;
            }
        }

        float diffuse = max( dot( s, norm ), 0.0 );

        lightColor += att * lightsArray[i].intensity * diffuse * lightsArray[i].color;
    }
    fragColor = vec4(col.rgb * lightColor, col.a);
}

传递给着色器的制服是：

qml: lightsArray[0].type = 0
qml: lightsArray[0].position = QVector3D(0, 10, 0)
qml: lightsArray[0].color = #ffffff
qml: lightsArray[0].intensity = 0.8
qml: lightsArray[0].constantAttenuation = 1
qml: lightsArray[0].linearAttenuation = 0
qml: lightsArray[0].quadraticAttenuation = 0
qml: lightsArray[1].type = 2
qml: lightsArray[1].position = QVector3D(0, 3, 0)
qml: lightsArray[1].color = #008000
qml: lightsArray[1].intensity = 0.5
qml: lightsArray[1].constantAttenuation = 2
qml: lightsArray[1].linearAttenuation = 0
qml: lightsArray[1].quadraticAttenuation = 0
qml: lightsArray[1].direction = QVector3D(-0.573576, -0.819152, 0)
qml: lightsArray[1].cutOffAngle = 15
qml: lightsNumber = 2

截屏：

Answer 1

对于聚光灯的光锥的原始可视化，您必须对视线和光锥进行交集。
以下算法在透视视图中工作，并且计算在视图（眼睛）空间中完成。该算法不关心场景的几何形状，也不做任何深度测试或阴影测试，它只是光锥的叠加可视化。

透视图中的视线可以由一个点和一个方向来定义。由于计算是在视图（眼睛）空间中完成的，因此该点是视点（视锥体的原点），即vec3(0.0).
通过视线和相机平截头体的近平面的交点，可以很容易地确定方向。如果片段的投影 XY 坐标在标准化设备坐标中已知（左下点为 (-1,-1)，右上点为 (1,1)，则可以轻松计算出此问题的答案）。

float aspect = .....; // ratio of the view port (widht/length)
float fov    = .....; // filed of view angle in radians (angle of the camera frustum on the Y-axis)
vec2  ndcPos = .....; // fragment position in NDC space from (-1,-1) to (1,1)

vec3 tanFov  = tan( fov * 0.5 );
vec3 los     = normalize( vec3( ndcPos.x * aspect * tanFov, ndcPos.y * tanFov, -1.0 ) );

光锥由光源的原点、光源指向的方向和光锥的全角定义。位置和方向必须在视图空间中向上。角度必须以弧度设置。

vec3  vLightPos = .....; // position of the light source in view space
vec3  vLightDir = .....; // direction of the light in view space 
float coneAngle = .....; // full angle of the light cone in radians

如何计算射线和圆锥的交点可以在 Stackoverflow 问题Points of intersection of vector with cone的答案和以下论文中找到：射线和圆锥的交点。
以下代码计算如上定义的射线和圆锥的交点。结果点存储在isectP. 如果有交集，则isIsect类型的变量设置为 1.0，否则设置为 0.0。float

// ray definition
vec3 O = vec3(0.0);
vec3 D = los;

// cone definition
vec3  C     = vLightPos;
vec3  V     = vLightDir;
float cosTh = cos( coneAngle * 0.5 );

// ray - cone intersection
vec3  CO     = O - C;
float DdotV  = dot( D, V );
float COdotV = dot( CO, V );
float a      = DdotV*DdotV - cosTh*cosTh;
float b      = 2.0 * (DdotV*COdotV - dot( D, CO )*cosTh*cosTh);
float c      = COdotV*COdotV - dot( CO, CO )*cosTh*cosTh;
float det    = b*b - 4.0*a*c;

// find intersection
float isIsect = 0.0;
vec3  isectP  = vec3(0.0);
if ( det >= 0.0 )
{
    vec3  P1 = O + (-b-sqrt(det))/(2.0*a) * D;
    vec3  P2 = O + (-b+sqrt(det))/(2.0*a) * D;
    float isect1 = step( 0.0, dot(normalize(P1-C), V) );
    float isect2 = step( 0.0, dot(normalize(P2-C), V) );
    P1 = mix( P2, P1, isect1 );
    isectP = P2.z < 0.0 && P2.z > P1.z ? P2 : P1;
    isIsect = mix( isect2, 1.0, isect1 ) * step( isectP.z, 0.0 );
}

有关完整的 GLSL 代码，请参阅以下 WebGL 示例：

(function loadscene() {

var sliderScale = 100.0
var gl, canvas, vp_size, camera, progDraw, progLightCone, bufTorus = {}, bufQuad = {}, drawFB;

function render(deltaMS) {

var ambient = document.getElementById( "ambient" ).value / sliderScale;
var diffuse = document.getElementById( "diffuse" ).value / sliderScale;
var specular = document.getElementById( "specular" ).value / sliderScale;
var shininess = document.getElementById( "shininess" ).value;
var cutOffAngle = document.getElementById( "cutOffAngle" ).value;

// setup view projection and model
vp_size = [canvas.width, canvas.height];
var prjMat = camera.Perspective();
var viewMat = camera.LookAt();
var modelMat = IdentM44();
modelMat = RotateAxis( modelMat, CalcAng( deltaMS, 13.0 ), 0 );
modelMat = RotateAxis( modelMat, CalcAng( deltaMS, 17.0 ), 1 );
    
var lightPos = [0.95, 0.95, -1.0];
var lightDir = [-1.0, -1.0, -3.0];
var lightCutOffAngleRad = cutOffAngle * Math.PI / 180.0;
var lightAtt = [0.7, 0.1, 0.5];

drawFB.Bind( true );    
gl.enable( gl.DEPTH_TEST );
gl.clearColor( 0.0, 0.0, 0.0, 1.0 );
gl.clear( gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT );

ShProg.Use( progDraw );
ShProg.SetM44( progDraw, "u_projectionMat44", prjMat );
ShProg.SetM44( progDraw, "u_viewMat44", viewMat );
ShProg.SetF3( progDraw, "u_light.position", lightPos );
ShProg.SetF3( progDraw, "u_light.direction", lightDir );
ShProg.SetF1( progDraw, "u_light.ambient", ambient );
ShProg.SetF1( progDraw, "u_light.diffuse", diffuse );
ShProg.SetF1( progDraw, "u_light.specular", specular );
ShProg.SetF1( progDraw, "u_light.shininess", shininess );
ShProg.SetF3( progDraw, "u_light.attenuation", lightAtt );
ShProg.SetF1( progDraw, "u_light.cutOffAngle", lightCutOffAngleRad );
ShProg.SetM44( progDraw, "u_modelMat44", modelMat );

bufObj = bufTorus;
gl.enableVertexAttribArray( progDraw.inPos );
gl.enableVertexAttribArray( progDraw.inNV );
gl.enableVertexAttribArray( progDraw.inCol );
gl.bindBuffer( gl.ARRAY_BUFFER, bufObj.pos );
gl.vertexAttribPointer( progDraw.inPos, 3, gl.FLOAT, false, 0, 0 );
gl.bindBuffer( gl.ARRAY_BUFFER, bufObj.nv );
gl.vertexAttribPointer( progDraw.inNV, 3, gl.FLOAT, false, 0, 0 ); 
gl.bindBuffer( gl.ARRAY_BUFFER, bufObj.col );
gl.vertexAttribPointer( progDraw.inCol, 3, gl.FLOAT, false, 0, 0 );
gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, bufObj.inx );
gl.drawElements( gl.TRIANGLES, bufObj.inxLen, gl.UNSIGNED_SHORT, 0 );
gl.disableVertexAttribArray( progDraw.pos );
gl.disableVertexAttribArray( progDraw.nv );
gl.disableVertexAttribArray( progDraw.col );

drawFB.Release( true );
gl.viewport( 0, 0, canvas.width, canvas.height );
var texUnitDraw = 2;
drawFB.BindTexture( texUnitDraw );
ShProg.Use( progLightCone );
ShProg.SetI1( progLightCone, "u_colorAttachment0", texUnitDraw );
ShProg.SetF2( progLightCone, "u_depthRange", [ camera.near, camera.far ] );
ShProg.SetF2( progLightCone, "u_vp", camera.vp );
ShProg.SetF1( progLightCone, "u_fov", camera.fov_y * Math.PI / 180.0 );
ShProg.SetF3( progLightCone, "u_light.position", lightPos );
ShProg.SetF3( progLightCone, "u_light.direction", lightDir );
ShProg.SetF3( progLightCone, "u_light.attenuation", lightAtt );
ShProg.SetF1( progLightCone, "u_light.cutOffAngle", lightCutOffAngleRad );

gl.enableVertexAttribArray( progLightCone.inPos );
gl.bindBuffer( gl.ARRAY_BUFFER, bufQuad.pos );
gl.vertexAttribPointer( progLightCone.inPos, 2, gl.FLOAT, false, 0, 0 );
gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, bufQuad.inx );
gl.drawElements( gl.TRIANGLES, bufQuad.inxLen, gl.UNSIGNED_SHORT, 0 );
gl.disableVertexAttribArray( progLightCone.inPos );

requestAnimationFrame(render);
}

function initScene() {

canvas = document.getElementById( "glow-canvas");
vp_size = [canvas.width, canvas.height];
gl = canvas.getContext( "experimental-webgl" );
if ( !gl )
    return;

document.getElementById( "ambient" ).value = 0.25 * sliderScale;
document.getElementById( "diffuse" ).value = 1.0 * sliderScale;
document.getElementById( "specular" ).value = 1.0 * sliderScale;
document.getElementById( "shininess" ).value = 10.0;
document.getElementById( "cutOffAngle" ).value = 30.0;

progDraw = ShProg.Create( 
    [ { source : "draw-shader-vs", stage : gl.VERTEX_SHADER },
    { source : "draw-shader-fs", stage : gl.FRAGMENT_SHADER }
    ] );

progDraw.inPos = ShProg.AttrI( progDraw, "inPos" );
progDraw.inNV  = ShProg.AttrI( progDraw, "inNV" );
progDraw.inCol = ShProg.AttrI( progDraw, "inCol" );
if ( progDraw == 0 )
    return;

progLightCone = ShProg.Create( 
    [ { source : "light-cone-shader-vs", stage : gl.VERTEX_SHADER },
    { source : "light-cone-shader-fs", stage : gl.FRAGMENT_SHADER }
    ] );
progLightCone.inPos = ShProg.AttrI( progDraw, "inPos" );
if ( progDraw == 0 )
    return;

var circum_size = 32, tube_size = 32;
var rad_circum = 1.5;
var rad_tube = 0.8;
var torus_pts = [];
var torus_nv = [];
var torus_col = [];
var torus_inx = [];
var col = [1, 0.5, 0.0];
for ( var i_c = 0; i_c < circum_size; ++ i_c ) {
    var center = [
        Math.cos(2 * Math.PI * i_c / circum_size),
        Math.sin(2 * Math.PI * i_c / circum_size) ]
    for ( var i_t = 0; i_t < tube_size; ++ i_t ) {
        var tubeX = Math.cos(2 * Math.PI * i_t / tube_size)
        var tubeY = Math.sin(2 * Math.PI * i_t / tube_size)
        var pt = [
            center[0] * ( rad_circum + tubeX * rad_tube ),
            center[1] * ( rad_circum + tubeX * rad_tube ),
            tubeY * rad_tube ]
        var nv = [ pt[0] - center[0] * rad_tube, pt[1] - center[1] * rad_tube, tubeY * rad_tube ]
        torus_pts.push( pt[0], pt[1], pt[2] );
        torus_nv.push( nv[0], nv[1], nv[2] );
        torus_col.push( col[0], col[1], col[2] );
        var i_cn = (i_c+1) % circum_size
        var i_tn = (i_t+1) % tube_size
        var i_c0 = i_c * tube_size; 
        var i_c1 = i_cn * tube_size; 
        torus_inx.push( i_c0+i_t, i_c0+i_tn, i_c1+i_t, i_c0+i_tn, i_c1+i_t, i_c1+i_tn )
    }
}
bufTorus.pos = gl.createBuffer();
gl.bindBuffer( gl.ARRAY_BUFFER, bufTorus.pos );
gl.bufferData( gl.ARRAY_BUFFER, new Float32Array( torus_pts ), gl.STATIC_DRAW );
bufTorus.nv = gl.createBuffer();
gl.bindBuffer( gl.ARRAY_BUFFER, bufTorus.nv );
gl.bufferData( gl.ARRAY_BUFFER, new Float32Array( torus_nv ), gl.STATIC_DRAW );
bufTorus.col = gl.createBuffer();
gl.bindBuffer( gl.ARRAY_BUFFER, bufTorus.col );
gl.bufferData( gl.ARRAY_BUFFER, new Float32Array( torus_col ), gl.STATIC_DRAW );
bufTorus.inx = gl.createBuffer();
gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, bufTorus.inx );
gl.bufferData( gl.ELEMENT_ARRAY_BUFFER, new Uint16Array( torus_inx ), gl.STATIC_DRAW );
bufTorus.inxLen = torus_inx.length;

bufQuad.pos = gl.createBuffer();
gl.bindBuffer( gl.ARRAY_BUFFER, bufQuad.pos );
gl.bufferData( gl.ARRAY_BUFFER, new Float32Array( [ -1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0 ] ), gl.STATIC_DRAW );
bufQuad.inx = gl.createBuffer();
gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, bufQuad.inx );
gl.bufferData( gl.ELEMENT_ARRAY_BUFFER, new Uint16Array( [ 0, 1, 2, 0, 2, 3 ] ), gl.STATIC_DRAW );
bufQuad.inxLen = 6;

camera = new Camera( [0, 4, 0.0], [0, 0, 0], [0, 0, 1], 90, vp_size, 0.5, 100 );

window.onresize = resize;
resize();
requestAnimationFrame(render);
}

function resize() {
//vp_size = [gl.drawingBufferWidth, gl.drawingBufferHeight];
vp_size = [window.innerWidth, window.innerHeight]
//vp_size = [256, 256]
canvas.width = vp_size[0];
canvas.height = vp_size[1];

var fbsize = Math.max(vp_size[0], vp_size[1]);
fbsize = 1 << 31 - Math.clz32(fbsize); // nearest power of 2

var fb_rect = [fbsize, fbsize];
drawFB = FrameBuffer.Create( fb_rect );
}

function Fract( val ) { 
return val - Math.trunc( val );
}
function CalcAng( deltaMS, intervall ) {
return Fract( deltaMS / (1000*intervall) ) * 2.0 * Math.PI;
}
function CalcMove( deltaMS, intervall, range ) {
var pos = self.Fract( deltaMS / (1000*intervall) ) * 2.0
var pos = pos < 1.0 ? pos : (2.0-pos)
return range[0] + (range[1] - range[0]) * pos;
}    

function IdentM44() { return [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]; }

function RotateAxis(matA, angRad, axis) {
var aMap = [ [1, 2], [2, 0], [0, 1] ];
var a0 = aMap[axis][0], a1 = aMap[axis][1]; 
var sinAng = Math.sin(angRad), cosAng = Math.cos(angRad);
var matB = matA.slice(0);
for ( var i = 0; i < 3; ++ i ) {
    matB[a0*4+i] = matA[a0*4+i] * cosAng + matA[a1*4+i] * sinAng;
    matB[a1*4+i] = matA[a0*4+i] * -sinAng + matA[a1*4+i] * cosAng;
}
return matB;
}

function Cross( a, b ) { return [ a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0], 0.0 ]; }
function Dot( a, b ) { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]; }
function Normalize( v ) {
var len = Math.sqrt( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
return [ v[0] / len, v[1] / len, v[2] / len ];
}

Camera = function( pos, target, up, fov_y, vp, near, far ) {
this.Time = function() { return Date.now(); }
this.pos = pos;
this.target = target;
this.up = up;
this.fov_y = fov_y;
this.vp = vp;
this.near = near;
this.far = far;
this.orbit_mat = this.current_orbit_mat = this.model_mat = this.current_model_mat = IdentM44();
this.mouse_drag = this.auto_spin = false;
this.auto_rotate = true;
this.mouse_start = [0, 0];
this.mouse_drag_axis = [0, 0, 0];
this.mouse_drag_angle = 0;
this.mouse_drag_time = 0;
this.drag_start_T = this.rotate_start_T = this.Time();
this.Ortho = function() {
var fn = this.far + this.near;
var f_n = this.far - this.near;
var w = this.vp[0];
var h = this.vp[1];
return [
    2/w, 0,   0,       0,
    0,   2/h, 0,       0,
    0,   0,   -2/f_n,  0,
    0,   0,   -fn/f_n, 1 ];
};  
this.Perspective = function() {
var n = this.near;
var f = this.far;
var fn = f + n;
var f_n = f - n;
var r = this.vp[0] / this.vp[1];
var t = 1 / Math.tan( Math.PI * this.fov_y / 360 );
return [
    t/r, 0, 0,          0,
    0,   t, 0,          0,
    0,   0, -fn/f_n,   -1,
    0,   0, -2*f*n/f_n, 0 ];
}; 
this.LookAt = function() {
var mz = Normalize( [ this.pos[0]-this.target[0], this.pos[1]-this.target[1], this.pos[2]-this.target[2] ] );
var mx = Normalize( Cross( this.up, mz ) );
var my = Normalize( Cross( mz, mx ) );
var tx = Dot( mx, this.pos );
var ty = Dot( my, this.pos );
var tz = Dot( [-mz[0], -mz[1], -mz[2]], this.pos ); 
return [mx[0], my[0], mz[0], 0, mx[1], my[1], mz[1], 0, mx[2], my[2], mz[2], 0, tx, ty, tz, 1]; 
};
} 

var FrameBuffer = {};
FrameBuffer.Create = function( vp, texturePlan ) {
var texPlan = texturePlan ? new Uint8Array( texturePlan ) : null;
var fb = gl.createFramebuffer();
fb.width = vp[0];
fb.height = vp[1];
gl.bindFramebuffer( gl.FRAMEBUFFER, fb );
fb.color0_texture = gl.createTexture();
gl.bindTexture( gl.TEXTURE_2D, fb.color0_texture );
gl.texImage2D( gl.TEXTURE_2D, 0, gl.RGBA, fb.width, fb.height, 0, gl.RGBA, gl.UNSIGNED_BYTE, texPlan );
gl.texParameteri( gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST );
gl.texParameteri( gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST );
fb.renderbuffer = gl.createRenderbuffer();
gl.bindRenderbuffer( gl.RENDERBUFFER, fb.renderbuffer );
gl.renderbufferStorage( gl.RENDERBUFFER, gl.DEPTH_COMPONENT16, fb.width, fb.height );
gl.framebufferTexture2D( gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, fb.color0_texture, 0 );
gl.framebufferRenderbuffer( gl.FRAMEBUFFER, gl.DEPTH_ATTACHMENT, gl.RENDERBUFFER, fb.renderbuffer );
gl.bindTexture( gl.TEXTURE_2D, null );
gl.bindRenderbuffer( gl.RENDERBUFFER, null );
gl.bindFramebuffer( gl.FRAMEBUFFER, null );

fb.Bind = function( clear ) {
    gl.bindFramebuffer( gl.FRAMEBUFFER, this );
    if ( clear ) {
        gl.viewport( 0, 0, this.width, this.height );
        gl.clearColor( 0.0, 0.0, 0.0, 1.0 );
        gl.clear( gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT );
    }
};

fb.Release = function( clear ) {
    gl.bindFramebuffer( gl.FRAMEBUFFER, null );
    if ( clear ) {
        gl.clearColor( 0.0, 0.0, 0.0, 1.0 );
        gl.clear( gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT );
    }
};

fb.BindTexture = function( textureUnit ) {
    gl.activeTexture( gl.TEXTURE0 + textureUnit );
    gl.bindTexture( gl.TEXTURE_2D, this.color0_texture );
};

return fb;
}

var ShProg = {};
ShProg.Create = function( shaderList ) {
var shaderObjs = [];
for ( var i_sh = 0; i_sh < shaderList.length; ++ i_sh ) {
    var shderObj = this.Compile( shaderList[i_sh].source, shaderList[i_sh].stage );
    if ( shderObj == 0 )
        return 0;
    shaderObjs.push( shderObj );
}
var progObj = this.Link( shaderObjs )
if ( progObj != 0 ) {
    progObj.attrInx = {};
    var noOfAttributes = gl.getProgramParameter( progObj, gl.ACTIVE_ATTRIBUTES );
    for ( var i_n = 0; i_n < noOfAttributes; ++ i_n ) {
        var name = gl.getActiveAttrib( progObj, i_n ).name;
        progObj.attrInx[name] = gl.getAttribLocation( progObj, name );
    }
    progObj.uniLoc = {};
    var noOfUniforms = gl.getProgramParameter( progObj, gl.ACTIVE_UNIFORMS );
    for ( var i_n = 0; i_n < noOfUniforms; ++ i_n ) {
        var name = gl.getActiveUniform( progObj, i_n ).name;
        progObj.uniLoc[name] = gl.getUniformLocation( progObj, name );
    }
}
return progObj;
}
ShProg.AttrI = function( progObj, name ) { return progObj.attrInx[name]; } 
ShProg.UniformL = function( progObj, name ) { return progObj.uniLoc[name]; } 
ShProg.Use = function( progObj ) { gl.useProgram( progObj ); } 
ShProg.SetI1  = function( progObj, name, val ) { if(progObj.uniLoc[name]) gl.uniform1i( progObj.uniLoc[name], val ); }
ShProg.SetF1  = function( progObj, name, val ) { if(progObj.uniLoc[name]) gl.uniform1f( progObj.uniLoc[name], val ); }
ShProg.SetF2  = function( progObj, name, arr ) { if(progObj.uniLoc[name]) gl.uniform2fv( progObj.uniLoc[name], arr ); }
ShProg.SetF3  = function( progObj, name, arr ) { if(progObj.uniLoc[name]) gl.uniform3fv( progObj.uniLoc[name], arr ); }
ShProg.SetF4  = function( progObj, name, arr ) { if(progObj.uniLoc[name]) gl.uniform4fv( progObj.uniLoc[name], arr ); }
ShProg.SetM44 = function( progObj, name, mat ) { if(progObj.uniLoc[name]) gl.uniformMatrix4fv( progObj.uniLoc[name], false, mat ); }
ShProg.Compile = function( source, shaderStage ) {
var shaderScript = document.getElementById(source);
if (shaderScript) {
    source = "";
    var node = shaderScript.firstChild;
    while (node) {
    if (node.nodeType == 3) source += node.textContent;
    node = node.nextSibling;
    }
}
var shaderObj = gl.createShader( shaderStage );
gl.shaderSource( shaderObj, source );
gl.compileShader( shaderObj );
var status = gl.getShaderParameter( shaderObj, gl.COMPILE_STATUS );
if ( !status ) alert(gl.getShaderInfoLog(shaderObj));
return status ? shaderObj : 0;
} 
ShProg.Link = function( shaderObjs ) {
var prog = gl.createProgram();
for ( var i_sh = 0; i_sh < shaderObjs.length; ++ i_sh )
    gl.attachShader( prog, shaderObjs[i_sh] );
gl.linkProgram( prog );
status = gl.getProgramParameter( prog, gl.LINK_STATUS );
if ( !status ) alert("Could not initialise shaders");
gl.useProgram( null );
return status ? prog : 0;
}
    
initScene();

})();

html,body { margin: 0; overflow: hidden; }
#gui { position : absolute; top : 0; left : 0; }

<script id="draw-shader-vs" type="x-shader/x-vertex">
precision mediump float;

attribute vec3 inPos;
attribute vec3 inNV;
attribute vec3 inCol;

varying vec3 vertPos;
varying vec3 vertNV;
varying vec3 vertCol;
varying vec4 clip_space_pos;
    
uniform mat4 u_projectionMat44;
uniform mat4 u_viewMat44;
uniform mat4 u_modelMat44;

void main()
{
    vec3 modelNV  = mat3( u_modelMat44 ) * normalize( inNV );
    vertNV        = mat3( u_viewMat44 ) * modelNV;
    vertCol       = inCol;
    vec4 modelPos = u_modelMat44 * vec4( inPos, 1.0 );
    vec4 viewPos  = u_viewMat44 * modelPos;
    vertPos       = viewPos.xyz / viewPos.w;
    gl_Position   = u_projectionMat44 * viewPos;
}
</script>

<script id="draw-shader-fs" type="x-shader/x-fragment">
precision mediump float;

varying vec3 vertPos;
varying vec3 vertNV;
varying vec3 vertCol;

struct Light {
    vec3  position;
    vec3  direction;
    float ambient;
    float diffuse;
    float specular;
    float shininess;
    vec3  attenuation;
    float cutOffAngle;
};
uniform Light u_light;

void main()
{
    vec3  color     = vertCol;
    vec3  lightCol  = u_light.ambient * color;
    vec3  normalV   = normalize( vertNV );
    vec3  lightV    = normalize( u_light.position - vertPos );
    float lightD    = length( u_light.position - vertPos );
    float cosL      = dot( normalize( u_light.direction ), -lightV );
    float inCone    = step( cos( u_light.cutOffAngle * 0.5 ), cosL );
    float att       = 1.0 / dot( vec3( 1.0, lightD, lightD*lightD ), u_light.attenuation );
    float NdotL     = max( 0.0, dot( normalV, lightV ) );
    lightCol       += NdotL * u_light.diffuse * color * inCone * att;
    vec3  eyeV      = normalize( -vertPos );
    vec3  halfV     = normalize( eyeV + lightV );
    float NdotH     = max( 0.0, dot( normalV, halfV ) );
    float kSpecular = ( u_light.shininess + 2.0 ) * pow( NdotH, u_light.shininess ) / ( 2.0 * 3.14159265 );
    lightCol       += kSpecular * u_light.specular * color * inCone * att;
    gl_FragColor    = vec4( lightCol.rgb, 1.0 );
}
</script>

<script id="light-cone-shader-vs" type="x-shader/x-vertex">
precision mediump float;
attribute vec2 inPos;
varying vec2 vertPos;
void main()
{
    vertPos.xy  = inPos.xy;
    gl_Position = vec4( inPos, 0.0, 1.0 );
}
</script>

<script id="light-cone-shader-fs" type="x-shader/x-fragment">
precision mediump float;

varying vec2 vertPos;

uniform sampler2D u_colorAttachment0;
uniform vec2  u_depthRange;
uniform vec2  u_vp;
uniform float u_fov;

struct Light {
    vec3  position;
    vec3  direction;
    float ambient;
    float diffuse;
    float specular;
    float shininess;
    vec3  attenuation;
    float cutOffAngle;
};
uniform Light u_light;

void main()
{
    vec4 texCol = texture2D( u_colorAttachment0, vertPos.st * 0.5 + 0.5 );
    
    vec3 vLightPos  = u_light.position;
    vec3 vLightDir  = normalize( u_light.direction );
    float tanFOV    = tan(u_fov*0.5);
    vec3  nearPos   = vec3( vertPos.x * u_vp.x/u_vp.y * tanFOV, vertPos.y * tanFOV, -1.0 );
    //vec2 texCoord = gl_FragCoord.xy / u_vp;
    //vec3 nearPos  = vec3( (texCoord.x-0.5) * u_vp.x/u_vp.y, texCoord.y-0.5, -u_depthRange.x );
    vec3 los        = normalize( nearPos );
    
    // ray definition
    vec3 O = vec3(0.0);
    vec3 D = los;

    // cone definition
    vec3  C     = vLightPos;
    vec3  V     = vLightDir;
    float cosTh = cos( u_light.cutOffAngle * 0.5 );
    
    // ray - cone intersection
    vec3  CO     = O - C;
    float DdotV  = dot( D, V );
    float COdotV = dot( CO, V );
    float a      = DdotV*DdotV - cosTh*cosTh;
    float b      = 2.0 * (DdotV*COdotV - dot( D, CO )*cosTh*cosTh);
    float c      = COdotV*COdotV - dot( CO, CO )*cosTh*cosTh;
    float det    = b*b - 4.0*a*c;
    
    // find intersection
    float isIsect = 0.0;
    vec3  isectP  = vec3(0.0);
    if ( det >= 0.0 )
    {
        vec3  P1 = O + (-b-sqrt(det))/(2.0*a) * D;
        vec3  P2 = O + (-b+sqrt(det))/(2.0*a) * D;
        float isect1 = step( 0.0, dot(normalize(P1-C), V) );
        float isect2 = step( 0.0, dot(normalize(P2-C), V) );
        if ( isect1 < 0.5 )
        {
            P1 = P2;
            isect1 = isect2;
        }
        if ( isect2 < 0.5 )
        {
            P2 = P1;
            isect2 = isect1;
        }
        isectP = ( P1.z > -u_depthRange.x || (P2.z < -u_depthRange.x && P1.z < P2.z ) ) ? P2 : P1;
        isIsect = mix( isect2, 1.0, isect1 ) * step( isectP.z, -u_depthRange.x );
    }
    
    float dist = length( isectP - vLightPos.xyz );
    float att  = 1.0 / dot( vec3( 1.0, dist, dist*dist ), u_light.attenuation );        
    
    
    gl_FragColor = vec4( mix( texCol.rgb, vec3(1.0, 1.0, 1.0), isIsect * att * 0.5 ), 1.0 );
}
</script>

<div><form id="gui" name="inputs">
<table>
    <tr> <td> <font color=#40f040>ambient</font> </td> 
            <td> <input type="range" id="ambient" min="0" max="100" value="0"/></td> </tr>
    <tr> <td> <font color=#40f040>diffuse</font> </td> 
            <td> <input type="range" id="diffuse" min="0" max="100" value="0"/></td> </tr>
    <tr> <td> <font color=#40f040>specular</font> </td> 
            <td> <input type="range" id="specular" min="0" max="100" value="0"/></td> </tr>
    <tr> <td> <font color=#40f040>shininess</font> </td> 
            <td> <input type="range" id="shininess" min="1" max="100" value="0"/></td> </tr>
    <tr> <td> <font color=#40f040>cut off angle</font> </td> 
            <td> <input type="range" id="cutOffAngle" min="1" max="180" value="0"/></td> </tr>
</table>
</form>
</div>

<canvas id="glow-canvas" style="border: none;"></canvas>