Silverlight Rotate & Scale a bitmap image to fit within rectangle without cropping

Question

I need to rotate a WriteableBitmap and scale it down or up before it gets cropped.

My current code will rotate but will crop the edges if the height is larger then the width.

I assume I need to scale?

 public WriteableBitmap Rotate(WriteableBitmap Source, double Angle)
        {
            RotateTransform rt = new RotateTransform();
            rt.Angle = Angle;

            TransformGroup transform = new TransformGroup();
            transform.Children.Add(rt);

            Image tempImage2 = new Image();
            WriteableBitmap wb;
            rt.CenterX = Source.PixelWidth / 2;
            rt.CenterY = Source.PixelHeight / 2;
            tempImage2.Width = Source.PixelWidth;
            tempImage2.Height = Source.PixelHeight;
            wb = new WriteableBitmap((int)(Source.PixelWidth), Source.PixelHeight);
            tempImage2.Source = Source;
            tempImage2.UpdateLayout();

            wb.Render(tempImage2, transform);
            wb.Invalidate();

            return wb;

        }

How do I scale down the image so it will not be cropped? Or is there another way?

Answer 1

You need to calculate the scaling based on the rotation of the corners relative to the centre.

If the image is a square only one corner is needed, but for a rectangle you need to check 2 corners in order to see if a vertical or horizontal edge is overlapped. This check is a linear comparison of how much the rectangle's height and width are exceeded.

Click here for the working testbed app created for this answer (image below):

double CalculateConstraintScale(double rotation, int pixelWidth, int pixelHeight)

The pseudo-code is as follows (actual C# code at the end):

• Convert rotation angle into Radians
• Calculate the "radius" from the rectangle centre to a corner
• Convert BR corner position to polar coordinates
• Convert BL corner position to polar coordinates
• Apply the rotation to both polar coordinates
• Convert the new positions back to Cartesian coordinates (ABS value)
• Find the largest of the 2 horizontal positions
• Find the largest of the 2 vertical positions
• Calculate the delta change for horizontal size
• Calculate the delta change for vertical size
• Return width/2 / x if horizontal change is greater
• Return height/2 / y if vertical change is greater

The result is a multiplier that will scale the image down to fit the original rectangle regardless of rotation.

**Note: While it is possible to do much of the maths using matrix operations, there are not enough calculations to warrant that. I also thought it would make a better example from first-principles.*

C# Code:

    /// <summary>
    /// Calculate the scaling required to fit a rectangle into a rotation of that same rectangle
    /// </summary>
    /// <param name="rotation">Rotation in degrees</param>
    /// <param name="pixelWidth">Width in pixels</param>
    /// <param name="pixelHeight">Height in pixels</param>
    /// <returns>A scaling value between 1 and 0</returns>
    /// <remarks>Released to the public domain 2011 - David Johnston (HiTech Magic Ltd)</remarks>
    private double CalculateConstraintScale(double rotation, int pixelWidth, int pixelHeight)
    {
        // Convert angle to radians for the math lib
        double rotationRadians = rotation * PiDiv180;

        // Centre is half the width and height
        double width = pixelWidth / 2.0;
        double height = pixelHeight / 2.0;
        double radius = Math.Sqrt(width * width + height * height);

        // Convert BR corner into polar coordinates
        double angle = Math.Atan(height / width);

        // Now create the matching BL corner in polar coordinates
        double angle2 = Math.Atan(height / -width);

        // Apply the rotation to the points
        angle += rotationRadians;
        angle2 += rotationRadians;

        // Convert back to rectangular coordinate
        double x = Math.Abs(radius * Math.Cos(angle));
        double y = Math.Abs(radius * Math.Sin(angle));
        double x2 = Math.Abs(radius * Math.Cos(angle2));
        double y2 = Math.Abs(radius * Math.Sin(angle2));

        // Find the largest extents in X & Y
        x = Math.Max(x, x2);
        y = Math.Max(y, y2);

        // Find the largest change (pixel, not ratio)
        double deltaX = x - width;
        double deltaY = y - height;

        // Return the ratio that will bring the largest change into the region
        return (deltaX > deltaY) ? width / x : height / y;
    }

Example of use:

    private WriteableBitmap GenerateConstrainedBitmap(BitmapImage sourceImage, int pixelWidth, int pixelHeight, double rotation)
    {
        double scale = CalculateConstraintScale(rotation, pixelWidth, pixelHeight);

        // Create a transform to render the image rotated and scaled
        var transform = new TransformGroup();
        var rt = new RotateTransform()
            {
                Angle = rotation,
                CenterX = (pixelWidth / 2.0),
                CenterY = (pixelHeight / 2.0)
            };
        transform.Children.Add(rt);
        var st = new ScaleTransform()
            {
                ScaleX = scale,
                ScaleY = scale,
                CenterX = (pixelWidth / 2.0),
                CenterY = (pixelHeight / 2.0)
            };
        transform.Children.Add(st);

        // Resize to specified target size
        var tempImage = new Image()
            {
                Stretch = Stretch.Fill,
                Width = pixelWidth,
                Height = pixelHeight,
                Source = sourceImage,
            };
        tempImage.UpdateLayout();

        // Render to a writeable bitmap
        var writeableBitmap = new WriteableBitmap(pixelWidth, pixelHeight);
        writeableBitmap.Render(tempImage, transform);
        writeableBitmap.Invalidate();
        return writeableBitmap;
    }

I released a Test-bed of the code on my website so you can try it for real - click to try it