How to get volume between terrain and curve plane

Questions
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1

Good day

please could you tell how to get the volume between terrain and curve plane

let a=100,b=100;
let p = new THREE.PlaneGeometry(50,50, a, b).rotateX(-Math.PI * 0.5);
let pos=p.vertices;
var ls =50; // length segments
var ws = width; // width segments, tracks
let trenchSpline = new THREE.CatmullRomCurve3([
new THREE.Vector3(vertices[0].x*0.25,vertices[0].z,vertices[0].y),
new THREE.Vector3(vertices[1].x*0.25,vertices[1].z,vertices[1].y),
new THREE.Vector3(vertices[2].x*0.25,vertices[2].z,vertices[2].y),
new THREE.Vector3(vertices[3].x*0.25,vertices[3].z,vertices[3].y),
]);
let trenchPoints = trenchSpline.getSpacedPoints(ls);
let m = new THREE.MeshBasicMaterial({color:'violet',wireframe:true});
let o = new THREE.Mesh(p, m);
scene.add(o);
var ht=0;
for(let x=0;x<100;x++){
for(let y=0;y<100;y++){
ht +=0.004
pos[y+100*x].y=Math.cos(ht)
}
}
var controls = new THREE.OrbitControls( camera, renderer.domElement );
var lss = ls + 1;
var wss = ws + 1;

var faceCount = ls * ws * 2;
var vertexCount = lss * wss;

var g = new THREE.BufferGeometry( );

g.faceIndices = new Uint32Array( faceCount * 3 );
g.vertices = new Float32Array( vertexCount * 3 );  
//g.normals = new Float32Array( vertexCount * 3 ); 
//g.uvs = new Float32Array( vertexCount * 2 );

g.setIndex( new THREE.BufferAttribute( g.faceIndices, 1 ) );	
g.addAttribute( 'position', new THREE.BufferAttribute( g.vertices, 3 ).setDynamic(true ) );
//g.addAttribute( 'normal', new THREE.BufferAttribute( g.normals, 3 ).setDynamic( true ) );
//g.addAttribute( 'uv', new THREE.BufferAttribute( g.uvs, 2 ) );

var idxCount = 0;
var material=new THREE.MeshBasicMaterial( { color: 'gray', side: THREE.DoubleSide, wireframe:false  } )
for ( var j = 0; j < ls; j ++ ) {
		
	for ( var i = 0; i < ws; i ++ ) {
	
		// 2 faces / segment,  3 vertex indices
		a =  wss * j+i;
		b1 = wss * ( j + 1 ) + i;		// right-bottom
		c1 = wss * ( j + 1 ) + 1 + i;
		b2 = wss * ( j + 1 ) + 1 + i;	// left-top
		c2 = wss * j + 1 + i;
		
		g.faceIndices[ idxCount     ] = a; // right-bottom
		g.faceIndices[ idxCount + 1 ] = b1;
		g.faceIndices[ idxCount + 2 ] = c1; 
		
		g.faceIndices[ idxCount + 3 ] = a; // left-top
		g.faceIndices[ idxCount + 4 ] = b2,
		g.faceIndices[ idxCount + 5 ] = c2; 
	
		g.addGroup( idxCount, 6, i ); // write groups for multi material
		
		idxCount += 6;
				
	}
		
}

var curveGeometry = new THREE.BufferGeometry().setFromPoints( points );
var tangent;
var normal = new THREE.Vector3( 0, 0, 0 );
var binormal = new THREE.Vector3( 0, 1, 0 );

var x, y, z;
var vIdx = 0; // vertex index
var posIdx; // position  index

for ( var j = 0; j < lss; j ++ ) {  // length
		
	for ( var i = 0; i < wss; i ++ ) { // width
		
		// calculate here the coordinates according to your wishes
		
		tangent = trenchSpline.getTangent( j / ls ); //  .. / length segments	
	
		normal.cross( tangent, binormal );

		binormal.cross( normal, tangent ); // new binormal
		
		normal.normalize().multiplyScalar(1 );
		x = trenchPoints[ j ].x+0.25*(i-ws/2)*normal.x; 
		y = trenchPoints[ j ].y;
		z = trenchPoints[ j ].z+0.25*(i-ws/2)*normal.z;
		
		xyzSet();
		
		vIdx ++;
		
	}
	
}

g.attributes.position.needsUpdate = true;
//g.attributes.normal.needsUpdate = true;

var mesh = new THREE.Mesh( g, material );
scene.add( mesh );
// set vertex position
function xyzSet() {
	
	posIdx = vIdx * 3;
	
	g.vertices[ posIdx ]  = x;
	g.vertices[ posIdx + 3 ]  = y;
	g.vertices[ posIdx + 2 ]  = z;

}
// volume between curve plane and terrain
for ( var j = 0; j < ls; j ++ ) {
		
	for ( var i = 0; i < ws; i ++ ) {
let thickness=0.25;

let V(cp)=new THREE.Triangle(a,b1,c1).getArea()*0.25;
let V(ter)=new THREE.Triangle(idx,idy,idz).getArea()*pos[i+100*j].y;
Vdif=Math.abs(Vcp-Vter)
}}

Capture
Capture1612×687 324 KB

2

Your topic revolves around integral calculus. I think you have to calculate that yourself, because I didn’t know that threejs does that for you. is that a sine wave? If you can tell me the boundary conditions, I’ll calculate it for you quickly. For this I need the amplitude of your wave and since your surface is inclined, the exact corner points of the surface that touch your wave

3

I got the amplitude of wave using cosinus I tried it with this code

var ht=0;
for(let x=0;x<100;x++){
for(let y=0;y<100;y++){
ht +=0.004
pos[y+100*x].y=Math.cos(ht)
}
}
4

I think I have to calculate that on paper first. I need to see the formula for this because calculating the area between a straight and a cosine wave is not difficult.