Measuring paths and groups of objects

Sometimes, it might be nececssary to measure a GraphicsPath object, either to determine a bounding box for the path, or to compute the path’s total length. Similarly, it can also be useful to determine a bounding box for all the objects contained on a Graphics surface.

Determining the bounding box of a GraphicsPath

The bounding box of a path is the smallest rectangle that contains all the points in the path. Note that this includes all the points through which the path passes, and not the control points of Bézier curves.

To compute the bounding box of a GraphicsPath object, you can use the GetBounds method:

GraphicsPath path = ...

// Compute the bounding box of the path.
Rectangle bounds = path.GetBounds();

This method returns a Rectangle object representing the bounding box of the path. Note that this does not include the path’s stroke (because the GraphicsPath does not contain any information about it - the stroke is applied when it is drawn on a Graphics object).

Since computing the bounding box can be relatively expensive, the result of this method is cached, so that if it is called multiple times, the actual computation only takes place once. The cached bounding box is invalidated when any element is added to the GraphicsPath.

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Determinining the bounding box of a Graphics

The Graphics class also implements a GetBounds method; this method determines the smallest rectangle that contains all the graphics elements that have been drawn on the surface. This bounding box also includes the thickness of the stroke of any path.

Graphics graphics = ...

// Draw something on graphics.

// Compute the bounding box of the graphics surface.
Rectangle bounds = graphics.GetBounds();

Note that, unlike the GraphicsPath.GetBounds method, the results of this method are not cached. However, since it internally invokes the GetBounds method of any GraphicsPath object that has been drawn on the Graphics, successive calls to this method should be relatively cheap anyways (because the bounding boxes of all elements have been cached).

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Cropping a Page

Once you have determined the bounding box of all the elements contained in a Graphics surface, you may also want to crop the corresponding page to that bounding box. This can be achieved using the Crop method of the Page object. This method will add an initial transformation to the page’s Graphics object so that the top-left corner of the bounding box of the Graphics lies at $\left (0, 0 \right)$, and change the Page’s size to the size of the bounding box.

For example, this code:

// The initial size does not matter.
Page page = new Page(1, 1);

// Draw a rectangle on the page's Graphics.
page.Graphics.FillRectangle(10, 10, 80, 80, Colours.Green);

// Crop the page.
page.Crop();

Is equivalent to:

// The size of the page is the same as the rectangle.
Page page = new Page(80, 80);

// Translation to place the top-left corner of the rectangle at (0, 0)
page.Graphics.Translate(-10, -10);

// Draw a rectangle on the page's Graphics.
page.Graphics.FillRectangle(10, 10, 80, 80, Colours.Green);

The Crop method has two overloads: one overload does not have any parameters, and crops the page to the bounding box of its Graphics; the other overload takes a Point and a Size defining the rectangular area to crop.

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Measuring the length of a GraphicsPath

It can also be interesting to measure the length of a GraphicsPath object in graphics units. This means, e.g., that the length of a segment going from $\left (x_1, y_1 \right)$ to $\left (x_2, y_2 \right)$ is $\sqrt{\left (x_1 -x_2 \right)^2 + \left (y_1 -y_2 \right)^2}$, or that the length of an arc segment with a radius of $r$ going from $\theta_1$ to $\theta_2$ is $\lvert \theta_2 - \theta_1 \rvert \cdot r$.

This can be achieved by using the MeasureLength method of the GraphicsPath class, which returns a double representing the length of the path:

GraphicsPath path = ...

// Compute the length of the path.
double length = path.MeasureLength();

Since there is no analytical formula to compute the length of a cubic Bézier curve, the length of any Bézier segments is computed by splitting the curve in many small straight segments, and summing the length of each segment. To ensure a decent precision in the estimate, the number of segments used is increased until the relative improvement in the estimate becomes smaller than $10^{-4}$.

As a result, this is also a rather expensive operation (especially on Blazor, this can be very slow). However, the results of the computation are cached at the segment level, so that repeated calls do not result in unnecessary computations.

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