diff -r f7dd937667a5 -r f99d52b1646b src/ui/canvas.cpp
--- a/src/ui/canvas.cpp	Fri Feb 28 19:24:33 2020 +0200
+++ b/src/ui/canvas.cpp	Sat Feb 29 23:43:38 2020 +0200
@@ -22,23 +22,17 @@
 	this->update();
 }
 
-QString vectorToString(const glm::vec3& vec)
-{
-	return "(%1, %2, %3)"_q
-		.arg(toDouble(vec.x))
-		.arg(toDouble(vec.y))
-		.arg(toDouble(vec.z));
-}
-
 void Canvas::mouseMoveEvent(QMouseEvent* event)
 {
 	const ldraw::Id id = this->pick(event->pos());
 	this->highlighted = id;
 	this->totalMouseMove += (event->pos() - this->lastMousePosition).manhattanLength();
-	this->worldPosition = this->screenToModelCoordinates(event->pos(), geom::XY);
+	this->worldPosition = this->screenToModelCoordinates(event->pos(), this->gridPlane);
 	if (this->worldPosition.has_value())
 	{
+		this->worldPosition = glm::inverse(this->gridMatrix) * glm::vec4{*this->worldPosition, 1};
 		this->worldPosition = glm::round(*this->worldPosition);
+		this->worldPosition = this->gridMatrix * glm::vec4{*this->worldPosition, 1};
 	}
 	if (this->worldPosition.has_value())
 	{
@@ -107,6 +101,13 @@
 		}
 	});
 	PartRenderer::initializeGL();
+	this->gridMatrix = glm::mat4{
+		{-4, 0, 0, 0},
+		{0, 6.9266, -3.6955, 0},
+		{0, -16.7222, -1.5307, 0},
+		{0, -13.273, -9.255, 1},
+	};
+	this->updateGridMatrix();
 }
 
 void Canvas::paintGL()
@@ -127,4 +128,31 @@
 		painter.setPen(Qt::white);
 		painter.drawText(pos + QPointF{5, 5}, vectorToString(*this->worldPosition));
 	}
+	{
+		QPainter axisPainter{this};
+		axisPainter.setRenderHint(QPainter::Antialiasing);
+		axisPainter.setPen(Qt::red);
+		axisPainter.drawLine(
+			this->modelToScreenCoordinates({10, 0, 0}),
+			this->modelToScreenCoordinates({-10, 0, 0}));
+		axisPainter.setPen(Qt::green);
+		axisPainter.drawLine(
+			this->modelToScreenCoordinates({0, 10, 0}),
+			this->modelToScreenCoordinates({0, -10, 0}));
+		axisPainter.setPen(Qt::blue);
+		axisPainter.drawLine(
+			this->modelToScreenCoordinates({0, 0, 10}),
+			this->modelToScreenCoordinates({0, 0, -10}));
+	}
 }
+
+void Canvas::updateGridMatrix()
+{
+	const geom::Triangle triangle {
+		this->gridMatrix * glm::vec4{0, 0, 0, 1},
+		this->gridMatrix * glm::vec4{1, 0, 0, 1},
+		this->gridMatrix * glm::vec4{0, 1, 0, 1},
+	};
+	this->gridPlane = geom::planeFromTriangle(triangle);
+	this->gridProgram->setGridMatrix(this->gridMatrix);
+}