WPF - Drawing on canvas with mouse events

I'm willing to bet that your canvas isn't receiving mouse events because it's background property is set to transparent

This works fine for me.

<Window x:Class="WpfApplication1.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">
    <Canvas  Name="paintSurface" MouseDown="Canvas_MouseDown_1" MouseMove="Canvas_MouseMove_1" >
        <Canvas.Background>
            <SolidColorBrush Color="White" Opacity="0"/>
        </Canvas.Background>
    </Canvas>
</Window>


using System;
using System.Threading;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Input;
using System.Windows.Shapes;

namespace WpfApplication1
{
    public partial class MainWindow : Window
    {

        Point currentPoint = new Point();

        public MainWindow()
        {
            InitializeComponent();
        }

        private void Canvas_MouseDown_1(object sender, System.Windows.Input.MouseButtonEventArgs e)
        {
            if (e.ButtonState == MouseButtonState.Pressed)
                currentPoint = e.GetPosition(this);
        }

        private void Canvas_MouseMove_1(object sender, System.Windows.Input.MouseEventArgs e)
        {
            if (e.LeftButton == MouseButtonState.Pressed)
            {
                Line line = new Line();

                line.Stroke = SystemColors.WindowFrameBrush;
                line.X1 = currentPoint.X;
                line.Y1 = currentPoint.Y;
                line.X2 = e.GetPosition(this).X;
                line.Y2 = e.GetPosition(this).Y;

                currentPoint = e.GetPosition(this);

                paintSurface.Children.Add(line);
            }
        }

    }
}

Simple use the InkCanvas

 <InkCanvas x:Name="InkCanvas" x:FieldModifier="public" Background="Transparent" Opacity="1" EditingMode="GestureOnly" ForceCursor="True" Cursor="Pen" >
                            <InkCanvas.DefaultDrawingAttributes>
                                <DrawingAttributes Color="White" Width="7" Height="7" />
                            </InkCanvas.DefaultDrawingAttributes>
                        </InkCanvas>

When using Line, thick line(line.StrokeThickness = 20) looks like this:

So I tried PolyLine and works fine.(from this example http://www.c-sharpcorner.com/uploadfile/mahesh/polyline-in-wpf/)

Canvas.MouseMove += (sender, args) =>
{
    if (args.LeftButton == MouseButtonState.Pressed)
    {
        Polyline polyLine;
        if (PathModeCanvas.Children.Count == 0)
        {
            polyLine = new Polyline();
            polyLine.Stroke = new SolidColorBrush(Colors.AliceBlue);
            polyLine.StrokeThickness = 10;

            Canvas.Children.Add(polyLine);
        }

        polyLine = (Polyline)Canvas.Children[0];
        Point currentPoint = args.GetPosition(Canvas);
        polyLine.Points.Add(currentPoint);
   }
};