Basic mountains
Mountains of my youth.
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// LL 2021
const seed = 0; // min=0 max=100 step=1
const subdiv_x = 160; // min=1 max=400 step=1
const subdiv_y = 110; // min=1 max=200 step=1
const scale = 150; // min=1 max=300 step=1
const height = 1; // min=0 max=2 step=0.01
const altitude = 0.7; // min=0 max=1 step=0.1
const perspective = 0.2; // min=0 max=1 step=0.01
const isometry = 0.2; // min=-1 max=1 step=0.01
const terrace = 0.0001; // min=0.0001 max=0.3 step=0.0001
const style = 1; // min=0 max=1 step=1 (Fast,Slow)
const show_grid = 0; // min=0 max=1 step=1 (No,Yes)
const offset_y = 30;
Canvas.setpenopacity(1);
const turtle = new Turtle();
var polygons = null;
console.clear();
var mix_t = 1;
class Mountain {
contructor() {
this.grid = [];
this.next_index = 0;
}
init() {
const size_x = subdiv_x + 1;
const size_y = subdiv_y + 1;
const multx=rng.nextFloat() * 2.5 + 0.5;
const multy=rng.nextFloat() * 2.5 + 0.5;
this.grid = Array.from({length: size_x*size_y}, (_,id) => {
const x = (id % size_x) / subdiv_x;
const y = Math.floor(id / size_x) / subdiv_y;
const ax = x * Math.PI * 2;
const ay = y * Math.PI * 2;
var peak = 0;
for (var i=1; i<=32; i*=2) {
peak += Math.cos(ax*i*multx) * Math.cos(ay*i*multy) / i;
}
peak *= 0.4;
peak = smin(peak, 0.3 + rng.nextFloat()*.005, 0.1);
peak = smax(peak, 0, 0.1);
const bell_spread = 0.25 * mix_t;
peak *= bell(x-0.5, 1, 0, bell_spread) * bell(y-0.5, 1, 0, bell_spread);
const wave_frequency = 6, wave_height = 0.01;
peak = smax(peak, Math.sin(ax * wave_frequency) * Math.sin(ay * wave_frequency) * wave_height, 0.1);
peak = Math.round(peak / terrace) * terrace;
const z = peak * height * mix_t;
return [ x - 0.5, -y, z ];
});
this.next_index = 0;
}
draw() {
if ((this.next_index % (subdiv_x+1)) == subdiv_x) this.next_index++;
const cell_count = show_grid ? 1 : subdiv_x;
if ((this.next_index + cell_count + subdiv_x + 1) > this.grid.length) return false;
const points = [];
for (var j = 0; j <= cell_count; j++) {
const k = j + this.next_index;
points.push([ this.grid[k][0], this.grid[k][1], this.grid[k][2] ]);
points.unshift([ this.grid[k + (subdiv_x+1)][0], this.grid[k + (subdiv_x+1)][1], this.grid[k + (subdiv_x+1)][2] ]);
}
this.next_index += cell_count;
points.forEach(p => {
p[0] *= 1 + perspective * p[1];
p[0] += isometry * p[1] + isometry * 0.5;
p[0] *= scale;
p[1] += 0.5;
p[1] *= altitude;
p[1] -= p[2];
p[1] *= scale;
p[1] += offset_y;
});
if (style == 0) {
turtle.jump(points[points.length-1]);
points.forEach(p=>turtle.goto(p));
} else {
const p1 = polygons.create();
p1.addPoints(...points);
//p1.addHatching(-Math.PI/4, 1);
p1.addOutline();
polygons.draw(turtle, p1, true);
}
return true;
}
}
function clamp(x, min, max) { return Math.min(max, Math.max(min, x)); }
function mix(x, y, a) { return x * (1-a) + y * a; }
function smin(a, b , s) { var h = clamp( 0.5 + 0.5*(b-a)/s, 0. , 1.); return mix(b, a, h) - h*(1.0-h)*s; }
function smax(a, b , s) { return -smin(-a, -b, s); }
// A: amplitude, B: phase, C: spread
function bell(x, a, b, c) {
if (c < 0.0001) return 0;
return a * Math.exp(((x-b)**2) / -(2*(c**2)));
}
const mountain = new Mountain();
function walk(i, t) {
if (i==0) {
mix_t = Math.cos(Math.pow(t,0.3)*Math.PI*2) * 0.5 + 0.5;
polygons = new Polygons();
mountain.init();
}
return mountain.draw();
}
////
function sleep(milliseconds) {
const date = Date.now();
let currentDate = null;
do {
currentDate = Date.now();
} while (currentDate - date < milliseconds);
}
//// Random with seed
function RNG(_seed) {
// LCG using GCC's constants
this.m = 0x80000000; // 2**31;
this.a = 1103515245;
this.c = 12345;
this.state = _seed ? _seed : Math.floor(Math.random() * (this.m - 1));
}
RNG.prototype.nextFloat = function() {
// returns in range [0,1]
this.state = (this.a * this.state + this.c) % this.m;
return this.state / (this.m - 1);
}
var rng = new RNG(seed);
////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////
function Polygons() {
const polygonList = [];
const Polygon = class {
constructor() {
this.cp = []; // clip path: array of [x,y] pairs
this.dp = []; // 2d lines [x0,y0],[x1,y1] to draw
this.aabb = []; // AABB bounding box
}
addPoints(...points) {
// add point to clip path and update bounding box
let xmin = 1e5, xmax = -1e5, ymin = 1e5, ymax = -1e5;
(this.cp = [...this.cp, ...points]).forEach( p => {
xmin = Math.min(xmin, p[0]), xmax = Math.max(xmax, p[0]);
ymin = Math.min(ymin, p[1]), ymax = Math.max(ymax, p[1]);
});
this.aabb = [(xmin+xmax)/2, (ymin+ymax)/2, (xmax-xmin)/2, (ymax-ymin)/2];
}
addSegments(...points) {
// add segments (each a pair of points)
points.forEach(p => this.dp.push(p));
}
addOutline() {
for (let i = 0, l = this.cp.length; i < l; i++) {
this.dp.push(this.cp[i], this.cp[(i + 1) % l]);
}
}
draw(t) {
for (let i = 0, l = this.dp.length; i < l; i+=2) {
t.jump(this.dp[i]), t.goto(this.dp[i + 1]);
}
}
addHatching(a, d) {
const tp = new Polygon();
tp.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);
const dx = Math.sin(a) * d, dy = Math.cos(a) * d;
const cx = Math.sin(a) * 200, cy = Math.cos(a) * 200;
for (let i = 0.5; i < 150 / d; i++) {
tp.dp.push([dx * i + cy, dy * i - cx], [dx * i - cy, dy * i + cx]);
tp.dp.push([-dx * i + cy, -dy * i - cx], [-dx * i - cy, -dy * i + cx]);
}
tp.boolean(this, false);
this.dp = [...this.dp, ...tp.dp];
}
inside(p) {
let int = 0; // find number of i ntersection points from p to far away
for (let i = 0, l = this.cp.length; i < l; i++) {
if (this.segment_intersect(p, [0.1, -1000], this.cp[i], this.cp[(i + 1) % l])) {
int++;
}
}
return int & 1; // if even your outside
}
boolean(p, diff = true) {
// bouding box optimization by ge1doot.
if (Math.abs(this.aabb[0] - p.aabb[0]) - (p.aabb[2] + this.aabb[2]) >= 0 &&
Math.abs(this.aabb[1] - p.aabb[1]) - (p.aabb[3] + this.aabb[3]) >= 0) return this.dp.length > 0;
// polygon diff algorithm (narrow phase)
const ndp = [];
for (let i = 0, l = this.dp.length; i < l; i+=2) {
const ls0 = this.dp[i];
const ls1 = this.dp[i + 1];
// find all intersections with clip path
const int = [];
for (let j = 0, cl = p.cp.length; j < cl; j++) {
const pint = this.segment_intersect(ls0, ls1, p.cp[j], p.cp[(j + 1) % cl]);
if (pint !== false) {
int.push(pint);
}
}
if (int.length === 0) {
// 0 intersections, inside or outside?
if (diff === !p.inside(ls0)) {
ndp.push(ls0, ls1);
}
} else {
int.push(ls0, ls1);
// order intersection points on line ls.p1 to ls.p2
const cmpx = ls1[0] - ls0[0];
const cmpy = ls1[1] - ls0[1];
int.sort( (a,b) => (a[0] - ls0[0]) * cmpx + (a[1] - ls0[1]) * cmpy -
(b[0] - ls0[0]) * cmpx - (b[1] - ls0[1]) * cmpy);
for (let j = 0; j < int.length - 1; j++) {
if ((int[j][0] - int[j+1][0])**2 + (int[j][1] - int[j+1][1])**2 >= 0.001) {
if (diff === !p.inside([(int[j][0]+int[j+1][0])/2,(int[j][1]+int[j+1][1])/2])) {
ndp.push(int[j], int[j+1]);
}
}
}
}
}
return (this.dp = ndp).length > 0;
}
//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
segment_intersect(l1p1, l1p2, l2p1, l2p2) {
const d = (l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) - (l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]);
if (d === 0) return false;
const n_a = (l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) - (l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]);
const n_b = (l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) - (l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]);
const ua = n_a / d;
const ub = n_b / d;
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) {
return [l1p1[0] + ua * (l1p2[0] - l1p1[0]), l1p1[1] + ua * (l1p2[1] - l1p1[1])];
}
return false;
}
};
return {
list: () => polygonList,
create: () => new Polygon(),
draw: (turtle, p, addToVisList=true) => {
for (let j = 0; j < polygonList.length && p.boolean(polygonList[j]); j++);
p.draw(turtle);
if (addToVisList) polygonList.push(p);
}
};
}