relativeInterfaceOrientationFromRotationAngle class extension for UIViewController

gistfile1.m

- (UIInterfaceOrientation)relativeInterfaceOrientationFromRotationAngle:(CGFloat)angle {
    NSArray * conversionMatrix = @[ @(UIInterfaceOrientationPortrait),
                                    @(UIInterfaceOrientationLandscapeRight),
                                    @(UIInterfaceOrientationPortraitUpsideDown),
                                    @(UIInterfaceOrientationMaskLandscapeLeft)];
    
    NSInteger oldIndex = [conversionMatrix indexOfObject:@(self.interfaceOrientation)];
    if (oldIndex == NSNotFound)
        return UIInterfaceOrientationUnknown;
    NSInteger newIndex = (oldIndex - (NSInteger)roundf(angle / M_PI_2)) % 4;
    while (newIndex < 0) {
        newIndex +=4;
    }
    return [conversionMatrix[newIndex] intValue];
}

Swift 4 conversion

    func relativeInterfaceOrientation(from rotationAngle: CGFloat) -> UIInterfaceOrientation {
        let conversionMatrix: [UIInterfaceOrientation] = [.portrait, .landscapeRight, .portraitUpsideDown, .landscapeLeft]
        guard let oldIndex = conversionMatrix.index(of: self.interfaceOrientation), oldIndex != NSNotFound else {
            return .unknown
        }
        var newIndex = Int(oldIndex) - Int(round(rotationAngle / .pi).truncatingRemainder(dividingBy: 4))
        while newIndex < 0 {
            newIndex += 4
        }
        return conversionMatrix[newIndex]
    }