Swept rectangle collision with time of impact

SweptRectangle.cs

//
// Copyright (c) 2019 João Baptista de Paula e Silva.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//

using System;
using Microsoft.Xna.Framework;

namespace SweptSAT
{
    public static class SweptRectangleTest
    {
        /// <summary>
        /// Returns the Time of Impact of the collision of two rectangles going at different velocities
        /// </summary>
        /// <param name="rect1">The first rectangle</param>
        /// <param name="v1">The velocity of the first rectangle</param>
        /// <param name="rect2">The second rectangle</param>
        /// <param name="v2">The velocity of the second rectangle</param>
        /// <returns>The time of impact of the collision, or NaN if no collision is detected.</returns>
        public static float TimeOfImpact(Rectangle rect1, Vector2 v1, Rectangle rect2, Vector2 v2)
        {
            // Top left and bottom right coordinates for the first rectangle
            var tl1 = new Vector2(rect1.X, rect1.Y);
            var br1 = tl1 + new Vector2(rect1.Width, rect1.Height);

            // Top left and bottom right coordinates for the second rectangle
            var tl2 = new Vector2(rect2.X, rect2.Y);
            var br2 = tl2 + new Vector2(rect2.Width, rect2.Height);

            // Relative velocities
            var vr = v2 - v1;

            // Return the maximum of both calculated times
            var toiX = TimeOfImpactSingleAxis(tl1.X, br1.X, tl2.X, br2.X, vr.X);
            var toiY = TimeOfImpactSingleAxis(tl1.Y, br1.Y, tl2.Y, br2.Y, vr.Y);
            return TimeInterval.Intersection(toiX, toiY).Begin;
        }

        /// <summary>
        /// Returns the Time of Impact of the collision of two intervals.
        /// The first interval is resting and the second is moving with a velocity v2.
        /// </summary>
        /// <param name="a1">First endpoint of first interval</param>
        /// <param name="b1">Second endpoint of first interval</param>
        /// <param name="a2">First endpoint of second interval</param>
        /// <param name="b2">Second endpoint of second interval</param>
        /// <param name="v2">Velocity of the second interval</param>
        /// <returns></returns>
        internal static TimeInterval TimeOfImpactSingleAxis(float a1, float b1, float a2, float b2, float v2)
        {
            // Get the two points in time where the intervals enter and leave intersection
            var k1 = (b1 - a2) / v2;
            var k2 = (a1 - b2) / v2;

            // Sort them to get an interval
            return new TimeInterval(Math.Min(k1, k2), Math.Max(k1, k2));
        }

        /// <summary>
        /// Represents a single time interval
        /// </summary>
        internal struct TimeInterval
        {
            public float Begin, End;

            public TimeInterval(float begin, float end)
            {
                Begin = begin;
                End = end;
            }

            public static TimeInterval Intersection(TimeInterval t1, TimeInterval t2)
            {
                var begin = Math.Max(t1.Begin, t2.Begin);
                var end = Math.Min(t1.End, t2.End);
                if (begin > end) begin = end = float.NaN;
                return new TimeInterval(begin, end);
            }
        }
    }
}