Missile simulator

Ballistic trajectory missile simulator.

A Javascript implementation of a missile simulator with GLSL shaders.

Description • How To Use • Demo • License

Description

The project renders a mesh of some hills with a missile. When start is pressed the missile completes a parabolic trajectory until it crash.

The position in the trajectory is calculated in 2D on a parabola and then projected into 3D space on a plane that lays on the start and end points.

A height parameter is used to modify the apex of the parabola.

function getParabolicPoint(start, end, height, completion) {
    //Ballistic trajectory
    const direction = utils.subVector(end, start)
    const normDirection = utils.normalizeVector3([direction[0], 0, direction[2]])
    const distance = utils.modulusVector3(direction)
    const g = 9.81 * height

    const alpha = Math.asin((end[1] - start[1]) / distance)
    const gamma = Math.atan2(0.5 * g * Math.cos(alpha), 0.5 * g * Math.sin(alpha) + distance) + alpha
    const v0 = 0.5 * g * Math.cos(alpha) / Math.sin(gamma - alpha)

    const x = v0 * completion * Math.cos(gamma)
    const y = v0 * completion * Math.sin(gamma) - 0.5 * g * Math.pow(completion, 2)

    return utils.sumVector(start, [x * normDirection[0], y, x * normDirection[2]])
}

To select the start and ending point a ray is unprojected from where the user clicked into the 3D world.

The ray vector (a point into 2D space is a line in 3D space) is extended utils.scalarVector3(dirNorm, 1000) to intersect the hills' mesh.

function unprojectScreenPoint(mesh, x, y) {
    //Ray-tracing algorithm
    const cm = getCameraAndMatrix()
    const worldMatrix = utils.MakeWorld(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1)
    const viewWorldMatrix = utils.multiplyMatrices(worldMatrix, cm.viewMatrix)
    const projectionMatrix = utils.multiplyMatrices(cm.perspectiveMatrix, viewWorldMatrix)

    const unprojectMatrix = utils.invertMatrix(projectionMatrix)
    const screenCoords = [x, y, 1.0, 1.0]
    const unprojectedRaypoint = utils.multiplyMatrixVector(unprojectMatrix, screenCoords)
    const normUnprojectedRaypoint = [unprojectedRaypoint[0] / unprojectedRaypoint[3],
        unprojectedRaypoint[1] / unprojectedRaypoint[3],
        unprojectedRaypoint[2] / unprojectedRaypoint[3]]

    const dirNorm = utils.normalizeVector3(utils.subVector(normUnprojectedRaypoint, cm.cameraPosition))
    const dirMax = utils.scalarVector3(dirNorm, 1000)
    const rayEnd = utils.sumVector(dirMax, cm.cameraPosition)
    return checkCollision(mesh, cm.cameraPosition, rayEnd)
}

To check is there was a collision between them is used the Möller–Trumbore algorithm, to cite Wikipedia:

The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle.

The point is later placed on the point where the collision happened.

function checkCollision(mesh, position, nextPosition) {
    //Möller–Trumbore algorithm
    const vertices = mesh.vertices, indices = mesh.indices, e = 0.0001
    for (let i = 0; i < indices.length; i += 3) {
        const v0 = [vertices[indices[i] * 3], vertices[indices[i] * 3 + 1], vertices[indices[i] * 3 + 2]]
        const v1 = [vertices[indices[i + 1] * 3], vertices[indices[i + 1] * 3 + 1], vertices[indices[i + 1] * 3 + 2]]
        const v2 = [vertices[indices[i + 2] * 3], vertices[indices[i + 2] * 3 + 1], vertices[indices[i + 2] * 3 + 2]]

        const v1_0 = utils.subVector(v1, v0)
        const v2_0 = utils.subVector(v2, v0)
        const h = utils.crossVector(nextPosition, v2_0)
        const a = utils.dotVector(v1_0, h)
        if (Math.abs(a) < e) continue

        const f = 1 / a
        const s = utils.subVector(position, v0)
        const u = f * utils.dotVector(s, h)
        if (u < 0.0 || u > 1.0) continue
        const q = utils.crossVector(s, v1_0)
        const v = f * utils.dotVector(nextPosition, q)
        if (v < 0.0 || u + v > 1.0) continue

        const t = f * utils.dotVector(v2_0, q)
        if (t > e) return utils.sumVector(position, utils.scalarVector3(nextPosition, t))
    }
    return false
}

How To Use

You can find it here.

Demo

License

MIT