You are on the right path. Check this link out on how to make your own color wheel and this post on how to use the canvas with angular. The solution is written in js using jquery so you can always update it to angular. It uses a canvas to draw the color wheel image and then the mousemove function (mouseover in angular) to get your pointer's current pixel rbg information. You can then use the click event to lock in the color you want.
$(function(){
// create canvas and context objects
var canvas = document.getElementById('picker');
var ctx = canvas.getContext('2d');
// drawing active image
var image = new Image();
image.onload = function () {
ctx.drawImage(image, 0, 0, image.width, image.height); // draw the image on the canvas
}
// select desired colorwheel
var imagesrc="images/colorwheel1.png";
switch ($(canvas).attr('var')) {
case '2':
imagesrc="images/colorwheel2.png";
break;
case '3':
imagesrc="images/colorwheel3.png";
break;
case '4':
imagesrc="images/colorwheel4.png";
break;
case '5':
imagesrc="images/colorwheel5.png";
break;
}
image.src = imageSrc;
$('#picker').mousemove(function(e) { // mouse move handler
if (bCanPreview) {
// get coordinates of current position
var canvasOffset = $(canvas).offset();
var canvasX = Math.floor(e.pageX - canvasOffset.left);
var canvasY = Math.floor(e.pageY - canvasOffset.top);
// get current pixel
var imageData = ctx.getImageData(canvasX, canvasY, 1, 1);
var pixel = imageData.data;
// update preview color
var pixelColor = "rgb("+pixel[0]+", "+pixel[1]+", "+pixel[2]+")";
$('.preview').css('backgroundColor', pixelColor);
// update controls
$('#rVal').val(pixel[0]);
$('#gVal').val(pixel[1]);
$('#bVal').val(pixel[2]);
$('#rgbVal').val(pixel[0]+','+pixel[1]+','+pixel[2]);
var dColor = pixel[2] + 256 * pixel[1] + 65536 * pixel[0];
$('#hexVal').val('#' + ('0000' + dColor.toString(16)).substr(-6));
}
});
});