Merge geometries, but use a single material - three.js

Question

Somewhat new to Three.js and 3d libraries in general.
I merged two geometries (a quarter cylinder and a plane) using this code:
var planeGeo = new THREE.PlaneGeometry(planeW, planeD / 2, 199, 399);
var planeMesh = new THREE.Mesh(planeGeo);
planeMesh.updateMatrix();
var cylinderGeo = new THREE.CylinderGeometry(100, 100, planeW, 199, 399, true, 0, Math.PI / 2);
cylinderGeo.rotateZ(Math.PI / 2).translate(0, 200, -100);
var cylinderMesh = new THREE.Mesh(cylinderGeo);
cylinderMesh.updateMatrix();
var singleGeometry = new THREE.Geometry();
singleGeometry.merge(planeMesh.geometry, planeMesh.matrix);
singleGeometry.merge(cylinderMesh.geometry, cylinderMesh.matrix);
var testmaterial = new THREE.MeshPhongMaterial({ color: 0x666666 });
mesh = new THREE.Mesh(singleGeometry, testmaterial);
scene.add(mesh);
I then would like to use a single material (png) over the entire thing. This code doesn't work:
textureLoader.load('data/test.png', function (texture) {
material = new THREE.MeshLambertMaterial({
map: texture
});
});
Later in the block with the merging...
mesh = new THREE.Mesh(singleGeometry, material);
scene.add(mesh);
This results in:
I would like the end result to be a single draped png over the entire merged geometry, but I can't find anything that suggests this is a normal thing to do. Is there a better way to achieve that result than merging geometries? Or am I just looking in the wrong places?

Answer 1

A poor-mans solution to achieve this, using the shape supplied in your post, is the following:
https://jsfiddle.net/87wg5z27/44/
Using code from this answer: https://stackoverflow.com/a/20774922/4977165
It sets the UVs based on the bounding box of the geometry, leaving out the z-coordinate (=0). Thats why the texture is a little bit stretched at the top, you can correct that manually or maybe its sufficent for you.
geometry.computeBoundingBox();
var max = geometry.boundingBox.max,
min = geometry.boundingBox.min;
var offset = new THREE.Vector2(0 - min.x, 0 - min.y);
var range = new THREE.Vector2(max.x - min.x, max.y - min.y);
var faces = geometry.faces;
geometry.faceVertexUvs[0] = [];
for (var i = 0; i < faces.length ; i++) {
var v1 = geometry.vertices[faces[i].a],
v2 = geometry.vertices[faces[i].b],
v3 = geometry.vertices[faces[i].c];
geometry.faceVertexUvs[0].push([
new THREE.Vector2((v1.x + offset.x)/range.x ,(v1.y + offset.y)/range.y),
new THREE.Vector2((v2.x + offset.x)/range.x ,(v2.y + offset.y)/range.y),
new THREE.Vector2((v3.x + offset.x)/range.x ,(v3.y + offset.y)/range.y)
]);
}
geometry.uvsNeedUpdate = true;