iphone - 使用 CATransform3D 将矩形图像转换为四边形

Question

我有一张图片和一组四个点(描述一个四边形 Q)。我想变换此图像，使其适合四边形 Q。Photoshop 将此变换称为“扭曲”。但根据这个四边形的来源(图像在空间中移动的视角)，它实际上是一个缩放、一个旋转和一个透视矩阵的组合。

我想知道使用 CATransform3D 4x4 矩阵是否可行。你有关于如何做到这一点的任何提示吗？我试图取这四个点并建立 16 个方程(从 A' = A x u 中得出)但它没有用:我不确定我应该使用什么作为 z、z'、w 和 w' 系数……

下图是我想做的:

这里有一些点的例子:

276.523, 236.438,   517.656, 208.945,   275.984, 331.285,   502.23,  292.344
261.441, 235.059,   515.09,  211.5,     263.555, 327.066,   500.734, 295
229.031, 161.277,   427.125, 192.562,   229.16, 226,        416.48,  256

Answer 1

我已经为在 iOS 上执行此操作创建了一个工具包:https://github.com/hfossli/AGGeometryKit/

---

确保你的 anchor 在左上角(CGPointZero)。

+ (CATransform3D)rectToQuad:(CGRect)rect
                     quadTL:(CGPoint)topLeft
                     quadTR:(CGPoint)topRight
                     quadBL:(CGPoint)bottomLeft
                     quadBR:(CGPoint)bottomRight
{
    return [self rectToQuad:rect quadTLX:topLeft.x quadTLY:topLeft.y quadTRX:topRight.x quadTRY:topRight.y quadBLX:bottomLeft.x quadBLY:bottomLeft.y quadBRX:bottomRight.x quadBRY:bottomRight.y];
}

+ (CATransform3D)rectToQuad:(CGRect)rect
                    quadTLX:(CGFloat)x1a
                    quadTLY:(CGFloat)y1a
                    quadTRX:(CGFloat)x2a
                    quadTRY:(CGFloat)y2a
                    quadBLX:(CGFloat)x3a
                    quadBLY:(CGFloat)y3a
                    quadBRX:(CGFloat)x4a
                    quadBRY:(CGFloat)y4a
{
    CGFloat X = rect.origin.x;
    CGFloat Y = rect.origin.y;
    CGFloat W = rect.size.width;
    CGFloat H = rect.size.height;

    CGFloat y21 = y2a - y1a;
    CGFloat y32 = y3a - y2a;
    CGFloat y43 = y4a - y3a;
    CGFloat y14 = y1a - y4a;
    CGFloat y31 = y3a - y1a;
    CGFloat y42 = y4a - y2a;

    CGFloat a = -H*(x2a*x3a*y14 + x2a*x4a*y31 - x1a*x4a*y32 + x1a*x3a*y42);
    CGFloat b = W*(x2a*x3a*y14 + x3a*x4a*y21 + x1a*x4a*y32 + x1a*x2a*y43);
    CGFloat c = H*X*(x2a*x3a*y14 + x2a*x4a*y31 - x1a*x4a*y32 + x1a*x3a*y42) - H*W*x1a*(x4a*y32 - x3a*y42 + x2a*y43) - W*Y*(x2a*x3a*y14 + x3a*x4a*y21 + x1a*x4a*y32 + x1a*x2a*y43);

    CGFloat d = H*(-x4a*y21*y3a + x2a*y1a*y43 - x1a*y2a*y43 - x3a*y1a*y4a + x3a*y2a*y4a);
    CGFloat e = W*(x4a*y2a*y31 - x3a*y1a*y42 - x2a*y31*y4a + x1a*y3a*y42);
    CGFloat f = -(W*(x4a*(Y*y2a*y31 + H*y1a*y32) - x3a*(H + Y)*y1a*y42 + H*x2a*y1a*y43 + x2a*Y*(y1a - y3a)*y4a + x1a*Y*y3a*(-y2a + y4a)) - H*X*(x4a*y21*y3a - x2a*y1a*y43 + x3a*(y1a - y2a)*y4a + x1a*y2a*(-y3a + y4a)));

    CGFloat g = H*(x3a*y21 - x4a*y21 + (-x1a + x2a)*y43);
    CGFloat h = W*(-x2a*y31 + x4a*y31 + (x1a - x3a)*y42);
    CGFloat i = W*Y*(x2a*y31 - x4a*y31 - x1a*y42 + x3a*y42) + H*(X*(-(x3a*y21) + x4a*y21 + x1a*y43 - x2a*y43) + W*(-(x3a*y2a) + x4a*y2a + x2a*y3a - x4a*y3a - x2a*y4a + x3a*y4a));

    const double kEpsilon = 0.0001;

    if(fabs(i) < kEpsilon)
    {
        i = kEpsilon* (i > 0 ? 1.0 : -1.0);
    }

    CATransform3D transform = {a/i, d/i, 0, g/i, b/i, e/i, 0, h/i, 0, 0, 1, 0, c/i, f/i, 0, 1.0};

    return transform;
}

此代码不归功于我。我所做的只是在互联网上搜索并将各种不完整的答案放在一起。