<a href="#" class="btn btn--show-overlay">Click me</a>

<div id="modal" class="modal">
    <button id="modal__close" class="modal__close">Close</button>
    <div id="svg-wrapper" class="svg-wrapper" data-btn-hovered="M1220.267,723.2c0,0-293.547,0-580.267,0c-333.653,0-584.533,0-584.533,0s0-104.783,0-334.854
  c0-188.981,0-334.846,0-334.846s251.733,0,584.533,0c362.667,0,580.267,0,580.267,0s0,116.7,0,344.803
  C1220.267,613.127,1220.267,723.2,1220.267,723.2L1220.267,723.2" data-modal-open="M1220.267,723.2c0,0-292.456-47.624-579.176-47.624c-333.653,0-585.624,47.624-585.624,47.624
  s83.149-104.783,83.149-334.854c0-188.981-83.149-334.846-83.149-334.846s251.324,49.105,584.124,49.105
  c362.667,0,580.676-49.105,580.676-49.105s-72.201,123.987-72.201,352.09C1148.065,620.414,1220.267,723.2,1220.267,723.2
  L1220.267,723.2">

      <svg id="svg" width="100%" height="100%" viewBox="0 0 1280 800"  preserveAspectRatio="none">
        <path id="svg-path" d="M1220.267,723.2c0,0-293.547,0-580.267,0c-333.653,0-584.533,0-584.533,0s0-3.505,0-11.2
  c0-6.321,0-11.2,0-11.2s251.733,0,584.533,0c362.667,0,580.267,0,580.267,0s0,3.903,0,11.533
  C1220.267,719.519,1220.267,723.2,1220.267,723.2L1220.267,723.2" />
      </svg>

    </div>
</div>
body {
  background-color: #FFF3F7;
  font-size: 16px;
  font-family: helvetica;
}

a {
  color: #2e2e2e;
  text-decoration: none;
  display: block;
  padding: 4px 8px;
  transition: color .25s ease-out;

  &:hover,
  &:focus {
    color: #FFF;
  }
}

.btn {
  text-align: center;
  z-index: 10;
  width: 250px;
  height: 105px;
  line-height: 96px;
  left: 50%;
  margin-left: -130px;
  font-weight: bold;
  text-transform: uppercase;
  position: absolute;
}

.svg-wrapper {
  position: absolute;
  width: 100%;
  height: 100%;
  top: 0;
  left: 0;

  svg {
    width: 100%;
    height: 100%;
    overflow: hidden;
  }
}

path {
  fill: #2e2e2e;
  stroke: #2e2e2e;
  stroke-width: 1px;
}

.modal {
  position: relative;
  margin: 0 auto;
  width: 250px;
  height: 105px;
  -webkit-transition: height 0.6s, width 0.6s;
  transition: height 0.6s, width 0.6s;
}

.modal__close {
  display: none;
  position: absolute;
  text-transform: uppercase;
  top: 65px;
  right: 85px;
  color: white;
  z-index: 10;
  border: none;
  background-color: transparent;
  border-bottom: 2px solid transparent;

  &:hover,
  &:focus {
    border-bottom-color: white;
  }
}

.modal--active {
  
  .modal {
    width: 100%;
    height: 630px;
  }
  
  .btn {
    display: none;
  }
  
  .modal__close {
    display: block;
  }
}
View Compiled
(function() {
  
  var svgModal = {
    showOverlay: $('.btn--show-overlay'),           
    closeOverlay: $('#modal__close'),
    modal: $('#modal'),                     
    svgWrapper: $("#svg-wrapper"),                 
    pathElement: undefined,
    modalOpen: false,
    btnHovered: false,                      
    paths: {
      default: $('#svg-path').attr('d'),            
      active: $("#svg-wrapper").data('btn-hovered'),      
      modalOpen: $('#svg-wrapper').data('modal-open')
    },
    init: function() {
      
      var s = Snap("#svg");
      
      svgModal.pathElement = s.select('path');
      this.events();                          
    },
    events: function() {
      svgModal.showOverlay.on('mouseenter', this.btnHover);
      svgModal.showOverlay.on('mouseleave', this.btnHover);
      svgModal.showOverlay.on('click', this.toggleModal);
      svgModal.closeOverlay.on('click', this.toggleModal);
    },
    btnHover: function(e) {
      e.preventDefault();
      
      var $this = $(this);
      
      if (!svgModal.modalOpen) {

        svgModal.pathElement.stop().animate({
          
          'path': svgModal.btnHovered ? svgModal.paths.default : svgModal.paths.active
          
        }, 250, mina.easeout);
        
        svgModal.btnHovered = !svgModal.btnHovered;
        
      }
    },
    toggleModal: function(e) {
      e.preventDefault();
      
      var $this = $(this);

      setTimeout(function() {
        $('body').toggleClass('modal--active');
      }, 100);
      
      svgModal.pathElement.stop().animate({
        
        'path': svgModal.paths.modalOpen
        
      }, 300, mina.easeout, function() {

        svgModal.pathElement.stop().animate({
          'path': svgModal.modalOpen ? svgModal.paths.active : svgModal.paths.default
        }, svgModal.modalOpen ? 800 : 300, svgModal.modalOpen ? mina.elastic : mina.easeout);

      });

      svgModal.btnHovered = false;

      svgModal.modalOpen = !svgModal.modalOpen;
      
    }
  };
  svgModal.init();
  
})();

External CSS

This Pen doesn't use any external CSS resources.

External JavaScript

  1. //cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js
  2. https://cdnjs.cloudflare.com/ajax/libs/snap.svg/0.3.0/snap.svg-min.js