public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }

    private bool isDragging;
    private void usercontrol_MouseDown(object sender, System.Windows.Input.MouseButtonEventArgs e)
    {
        bre.CaptureMouse();
        isDragging = true;

    }

    private void usercontrol_MouseMove(object sender, System.Windows.Input.MouseEventArgs e)
    {
        if (isDragging)
        {
            Point canvPosToWindow = canv.TransformToAncestor(this).Transform(new Point(0, 0));

            UserControl1 r = sender as UserControl1;
            var upperlimit = canvPosToWindow.Y + (r.Height / 2);
            var lowerlimit = canvPosToWindow.Y + canv.ActualHeight - (r.Height / 2);

            var leftlimit = canvPosToWindow.X + (r.Width / 2);
            var rightlimit = canvPosToWindow.X + canv.ActualWidth - (r.Width / 2);

            var absmouseXpos = e.GetPosition(this).X;
            var absmouseYpos = e.GetPosition(this).Y;

            if ((absmouseXpos > leftlimit && absmouseXpos < rightlimit)
                && (absmouseYpos > upperlimit && absmouseYpos < lowerlimit))
            {
                r.SetValue(Canvas.LeftProperty, e.GetPosition(canv).X - (r.Width / 2));
                r.SetValue(Canvas.TopProperty, e.GetPosition(canv).Y - (r.Height / 2));
            }
        }
    }
    private void usercontrol_MouseUp(object sender, System.Windows.Input.MouseButtonEventArgs e)
    {
        bre.ReleaseMouseCapture();
        isDragging = false;
    }
}

<Window x:Class="WpfApplication6.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    xmlns:local="clr-namespace:WpfApplication6"
    mc:Ignorable="d"
    Title="MainWindow" Height="350" Width="525">
<Grid>

<Canvas x:Name="canv"  Background="#FF131315" Margin="104,27,103,10">
    <local:UserControl1  x:Name="bre" Canvas.Left="81" Canvas.Top="31" Width="166" />
</Canvas>

<UserControl x:Class="WpfApplication6.UserControl1"
         xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
         xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
         xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
         xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
         xmlns:local="clr-namespace:WpfApplication6"
         mc:Ignorable="d"
         d:DesignHeight="300" d:DesignWidth="300">
    <Grid  Name="bre">
        <Ellipse x:Name="circleUI" Height="100" Width="100"
                 Fill="Blue" />
    </Grid>
</UserControl>

{
    public UserControl1()
    {
        InitializeComponent();
    }

    public UserControl1(UserControl1 c)
    {
        InitializeComponent();
        this.circleUI.Height = c.circleUI.Height;
        this.circleUI.Width = c.circleUI.Height;
        this.circleUI.Fill = c.circleUI.Fill;
    }
}