着色器 - 通过“拉”像素来反鱼眼

Question

我想修复这张图片的失真：

对不起质量，但这是我能找到的最好的例子。

我不知道是否可以修复这种失真（我想要直门和直天花板），但基本上，不是将像素推到图像之外（红色箭头），而是添加模糊效果，我想做相反的事情（绿色箭头），将像素拉向中心。

如果你有任何想法，那就太棒了。也欢迎其他解决方案！

Answer 1

为了定义鱼眼效果，您必须将角度 (alpha) 与视口的对角线 (d) 相关联。
视口的对角线是圆的直径，包括整个视口。

周长圆的半径（r）与角度（alpha）的关系为：

r = tan(alpha / 2)

下面eye_angle对应alpha，half_dist对应r：

float half_angle = eye_angle/2.0;
float half_dist = tan(half_angle);

使用视口的纵横比 (aspect) 并且是片段在视口ndcPos 上的标准化设备位置，可以计算出位置P。在标准化设备空间中，x 和 y 在范围 [-1, 1] 内：

vec2 vp_scale = vec2(aspect, 1.0);
vec2 P = ndcPos * vp_scale; 

对于视口上的每个点 (P)，必须计算与视口中心相对于周边圆的相对距离 (rel_dist)。并且需要点（P）与纵横比的相对位置（rel_P）：

float vp_dia   = length(vp_scale);
float rel_dist = length(P) / vp_dia;  
vec2  rel_P    = normalize(P) / normalize(vp_scale);

鱼眼效果是由球面在平面上的投影引起的。为了计算从和到投影的距离，必须找到弧长和到平面中心的距离之间的关系：

如果圆的半径为 1，则圆弧的长度等于圆弧段的角度（以弧度为单位）。所以到点P的距离和角度beta的关系是：

|P|/r = tan(beta)
beta = atan(|P|/r)

如果从球面到平面的投影是：

float beta    = rel_dist * half_angle;
vec3  pos_prj = rel_P * tan(beta) / half_dist;  

而从平面到球面的投影为：

float beta    = atan(rel_dist * half_dist);
vec2  pos_prj = rel_P * beta / half_angle;

请参阅以下 WebGL 示例，该示例使用片段着色器来实现算法。角度 alpha 设置为统一变量u_alpha。
如果u_alpha > 0.0，则计算球面到平面的投影。
如果u_alpha < 0.0，则计算平面到球面的投影。

(function loadscene() {    

var canvas, gl, vp_size, texture, prog, bufObj = {};

function initScene() {

    canvas = document.getElementById( "ogl-canvas");
    gl = canvas.getContext( "experimental-webgl" );
    if ( !gl )
      return;

    texture = new Texture( "https://raw.githubusercontent.com/Rabbid76/graphics-snippets/master/resource/texture/supermario.jpg" ); 
    texture.bound = false;

    progDraw = gl.createProgram();
    for (let i = 0; i < 2; ++i) {
        let source = document.getElementById(i==0 ? "draw-shader-vs" : "draw-shader-fs").text;
        let shaderObj = gl.createShader(i==0 ? gl.VERTEX_SHADER : gl.FRAGMENT_SHADER);
        gl.shaderSource(shaderObj, source);
        gl.compileShader(shaderObj);
        let status = gl.getShaderParameter(shaderObj, gl.COMPILE_STATUS);
        if (!status) alert(gl.getShaderInfoLog(shaderObj));
        gl.attachShader(progDraw, shaderObj);
        gl.linkProgram(progDraw);
    }
    status = gl.getProgramParameter(progDraw, gl.LINK_STATUS);
    if ( !status ) alert(gl.getProgramInfoLog(progDraw));
    progDraw.inPos = gl.getAttribLocation(progDraw, "inPos");
    progDraw.u_time = gl.getUniformLocation(progDraw, "u_time");
    progDraw.u_resolution = gl.getUniformLocation(progDraw, "u_resolution");
    progDraw.u_texture = gl.getUniformLocation(progDraw, "u_texture");
    progDraw.u_angle = gl.getUniformLocation(progDraw, "u_angle");
    gl.useProgram(progDraw);

    var pos = [ -1, -1, 1, -1, 1, 1, -1, 1 ];
    var inx = [ 0, 1, 2, 0, 2, 3 ];
    bufObj.pos = gl.createBuffer();
    gl.bindBuffer( gl.ARRAY_BUFFER, bufObj.pos );
    gl.bufferData( gl.ARRAY_BUFFER, new Float32Array( pos ), gl.STATIC_DRAW );
    bufObj.inx = gl.createBuffer();
    bufObj.inx.len = inx.length;
    gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, bufObj.inx );
    gl.bufferData( gl.ELEMENT_ARRAY_BUFFER, new Uint16Array( inx ), gl.STATIC_DRAW );
    gl.enableVertexAttribArray( progDraw.inPos );
    gl.vertexAttribPointer( progDraw.inPos, 2, gl.FLOAT, false, 0, 0 ); 
    
    gl.enable( gl.DEPTH_TEST );
    gl.clearColor( 0.0, 0.0, 0.0, 1.0 );

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

function resize() {
    vp_size = [window.innerWidth, window.innerHeight];
    canvas.width = vp_size[0];
    canvas.height = vp_size[1];
}

function render(deltaMS) {

    scale = document.getElementById( "scale" ).value / 100 * 2.0 - 1.0;

    gl.viewport( 0, 0, canvas.width, canvas.height );
    gl.clear( gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT );
   
    texture.bound = texture.bound || texture.bind( 0 );
    gl.uniform1i(progDraw.u_texture, 0);
    gl.uniform1f(progDraw.u_time, deltaMS/2000.0);
    gl.uniform2f(progDraw.u_resolution, canvas.width, canvas.height);
    gl.uniform1f(progDraw.u_angle, scale * Math.PI * 0.9);
    gl.drawElements( gl.TRIANGLES, bufObj.inx.len, gl.UNSIGNED_SHORT, 0 );
    
    requestAnimationFrame(render);
}  

class Texture {
    constructor( name, dflt ) {
        let texture = this;
        this.dflt = dflt || [128,128,128,255]
        let image = { "cx": this.dflt.w || 1, "cy": this.dflt.h || 1, "plane": this.dflt.p || this.dflt };
        this.size = [image.cx, image.cy];
        this.dummyObj = Texture.createTexture2D( image, true )
        this.image = new Image(64,64);
        this.image.setAttribute('crossorigin', 'anonymous');
        this.image.onload = function () {
            let cx = 1 << 31 - Math.clz32(texture.image.naturalWidth);
            if ( cx < texture.image.naturalWidth ) cx *= 2;
            let cy = 1 << 31 - Math.clz32(texture.image.naturalHeight);
            if ( cy < texture.image.naturalHeight ) cy *= 2;
            var canvas = document.createElement( 'canvas' );
            canvas.width  = cx;
            canvas.height = cy;
            var context = canvas.getContext( '2d' );
            context.drawImage( texture.image, 0, 0, canvas.width, canvas.height );
            texture.textureObj = Texture.createTexture2D( canvas, true );
            texture.size = [cx, cy];
        }
        this.image.src = name;
    }
    static createTexture2D( image, flipY ) {
        let t = gl.createTexture();
        gl.activeTexture( gl.TEXTURE0 );
        gl.bindTexture( gl.TEXTURE_2D, t );
        gl.pixelStorei( gl.UNPACK_FLIP_Y_WEBGL, flipY != undefined && flipY == true );
        if ( image.cx && image.cy && image.plane )
            gl.texImage2D( gl.TEXTURE_2D, 0, gl.RGBA, image.cx, image.cy, 0, gl.RGBA, gl.UNSIGNED_BYTE, new Uint8Array(image.plane) );
        else
            gl.texImage2D( gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, image );
        gl.texParameteri( gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR );
        gl.texParameteri( gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR );
        gl.texParameteri( gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.REPEAT );
        gl.texParameteri( gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.REPEAT );
        gl.bindTexture( gl.TEXTURE_2D, null );
        return t;
    }
    bind( texUnit = 0 ) {
        gl.activeTexture( gl.TEXTURE0 + texUnit );
        if ( this.textureObj ) { 
            gl.bindTexture( gl.TEXTURE_2D, this.textureObj );
            return true;
        }
        gl.bindTexture( gl.TEXTURE_2D, this.dummyObj );
        return false;
    }
};

initScene();

})();

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

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

uniform float     u_time;
uniform vec2      u_resolution;
uniform float     u_angle;
uniform sampler2D u_texture;

void main()
{
    vec2 uv = gl_FragCoord.xy / u_resolution;
    vec2 ndcPos = uv * 2.0 - 1.0;

    float aspect = u_resolution.x / u_resolution.y;
    
    float eye_angle = abs(u_angle);
    float half_angle = eye_angle/2.0;
    float half_dist = tan(half_angle);

    vec2  vp_scale = vec2(aspect, 1.0);
    vec2  P = ndcPos * vp_scale; 
    
    float vp_dia   = length(vp_scale);
    float rel_dist = length(P) / vp_dia;  
    vec2  rel_P = normalize(P) / normalize(vp_scale);

    vec2 pos_prj = ndcPos;
    if (u_angle > 0.0)
    {
        float beta = rel_dist * half_angle;
        pos_prj = rel_P * tan(beta) / half_dist;  
    }
    else if (u_angle < 0.0)
    {
        float beta = atan(rel_dist * half_dist);
        pos_prj = rel_P * beta / half_angle;
    }

    vec2 uv_prj = pos_prj * 0.5 + 0.5;
    vec2 rangeCheck = step(vec2(0.0), uv_prj) * step(uv_prj, vec2(1.0));   
    if (rangeCheck.x * rangeCheck.y < 0.5)
        discard;

    vec4 texColor = texture2D(u_texture, uv_prj.st);
    gl_FragColor = vec4( texColor.rgb, 1.0 );
}
</script>

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

attribute vec2 inPos;

void main()
{
    gl_Position = vec4( inPos.xy, 0.0, 1.0 );
}
</script>

<canvas id="ogl-canvas" style="border: none"></canvas>
<form id="gui" name="inputs">
<input type="range" id="scale" min="0" max="100" value="20"/>
</form>

Answer 2

这种失真是相机的特性。如果您可以使用用于拍照的相机，则可以对其进行校准以提取其应用的变形。否则，您仍然可以使用一些通用方程。看看 Paul Bourke 的 article、这个 Stack Overflow answer 或这个 Shader Toy example，看看它是如何实现的。