var view = new ol.View();
var map = new ol.Map({
layers: [ new ol.layer.Tile({ source: new ol.source.OSM() }) ],
target: 'map'
});
function openMap() {
map.setView(view);
var extent = ol.proj.transformExtent([ -540, -85, 540, 85], 'EPSG:4326', 'EPSG:3857');
// fit the extent horizontally or vertically depending on screen size
// to determine the maximum resolution possible
var size = map.getSize();
var width = ol.extent.getWidth(extent);
var height = ol.extent.getHeight(extent);
if (size[0]/size[1] > width/height) {
view.fit([extent[0],(extent[1]+extent[3])/2,extent[2],(extent[1]+extent[3])/2], { constrainResolution: false });
} else {
view.fit([(extent[0]+extent[2])/2,extent[1],(extent[0]+extent[2])/2,extent[3]], { constrainResolution: false });
}
var maxResolution = view.getResolution();
var resolution = 0;
function resChange() {
var oldView = map.getView();
if (resolution == 0 || oldView.getZoom()%1 == 0) {
resolution = oldView.getResolution();
var width = map.getSize()[0] * resolution;
var height = map.getSize()[1] * resolution;
var newView = new ol.View({
projection: oldView.getProjection(),
extent: [extent[0]+(width/2), extent[1]+(height/2), extent[2]-(width/2), extent[3]-(height/2)],
resolution: resolution,
maxResolution: maxResolution,
rotation: oldView.getRotation()
});
newView.setCenter(newView.constrainCenter(oldView.getCenter()));
newView.on('change:resolution', resChange);
map.setView(newView);
}
}
resChange();
}
map.on('change:size', openMap);
openMap();
<link rel="stylesheet" href="https://cdn.rawgit.com/openlayers/openlayers.github.io/master/en/v5.3.0/css/ol.css" type="text/css">
<script src="https://cdn.rawgit.com/openlayers/openlayers.github.io/master/en/v5.3.0/build/ol.js"></script>
<div id="map" class="map"></div>