• The Idea:
  • Many programs need to center content of some kind in a container of some kind
• An Example:
  • Text within a line (so it needs to find the column in where the text should start)

• A Limitation of Console Output:
  • You can't specify the column
• A Work-Around:
  • Create a String that has the appropriate number of spaces before the text

• A Specific Example:
  • The line is 9 characters wide and 0-based
  • The text is 5 characters wide and 0-based
• Some Implications:
  • The middle character in the line has index 4
  • The middle character of the text has index 2
• A Solution to this Specific Example:
  • Character 2 of the text has to be at position 4 of the line, meaning character 0 of the text must be at position 2 of the line (i.e., there must be two leading spaces)

• Notation:
  • \(C\) denotes the container (a generalization of the line)
  • \(c\) denotes the content (a generalization of the text)
  • \(E\) denotes the extent (a generalization of the width)
  • \(M\) denotes the mid-point
  • \(R\) denotes the reference (a generalization of the starting character)
• The Equations (for Each Dimension):
  • \(C^M = C^R + (C^E / 2)\)
  • \(c^M = (c^E / 2)\)
  • \(c^R = c^M - (c^E / 2)\)

javaexamples/programmingpatterns/Centering.java (Fragment: one)

            /**
     * Calculate the reference point (in 1 dimension) for a piece of
     * content with given extent (in 1 dimension) in such a way that it will
     * be centered around a container with a given reference point and
     * extend.
     *
     * @param containerReference  The reference point of the container
     * @param containerExtent     The extent of the container
     * @param contentExtent       The extent of the content
     * @return                    The reference point of the content
     */
    public static double center(double containerReference, 
                                double containerExtent,
                                double contentExtent) {
        double containerMidpoint = containerReference + containerExtent / 2.0;
        double contentMidpoint = contentExtent / 2.0;
        double contentReference = containerMidpoint -  contentMidpoint;
        
        return contentReference;
    }
        

javaexamples/programmingpatterns/Centering.java (Fragment: multi)

            /**
     * Calculate the reference point (in n dimensions) for a piece of
     * content with given extent (in n dimensions) in such a way that it will
     * be centered around a container with a given reference point and
     * extend.
     *
     * @param containerReference  The reference point of the container
     * @param containerExtent     The extent of the container
     * @param contentExtent       The extent of the content
     * @return                    The reference point of the content
     */
    public static double[] center(double[] containerReference, 
                                  double[] containerExtent,
                                  double[] contentExtent) {
        int n = containerReference.length;        
        double[] contentReference = new double[n];
        
        for (int i = 0; i < n; ++i) {
            double containerMidpoint = containerReference[i]
                + containerExtent[i] / 2.0;
            
            double contentMidpoint = contentExtent[i] / 2.0;
            
            contentReference[i] = containerMidpoint -  contentMidpoint;
        }
        return contentReference;
    }
        

• Coordinate Systems:
  • These examples use Euclidean coordinates but computer displays use screen coordinates
• Discrete Sets:
  • If the content/container are discrete (i.e., use integer sizes and positions) then the content may have to "lean" to the left or right
• Clipping:
  • The container may not be large enough to hold the content in which case it may need to be clipped