How to Find Minimum Area Bounding Rectangle for given 3D Polygon ?

I have an arbitrary polygon as shown in Pic with co-planar Vertices's A,B,C,D,E,F,G,H in 3 D coordinate System. This Polygon is about to arbitrary axis.

Step 1. Rotate Arbitrary Polygon in X-Y Plane[Bounding-rectangle of 3D Polygon]

Step 2. Pick 1 edge and align this edge with the X axis(use Destination Vector " Vector3(1, 0, 0); // X-axis for align Edge Along X-axis " and Edge Direction as Source Vector. Compute Rotation Matrix and Save as EdgeAlignX-Axis Matrix to Rotate back Rectangle in Step 4). Use the min/max x,y to find the bounding rectangle. Compute Area and store in list, Do the same for remaining edges in  polygon. Pick the rectangle with the minimum Area.

Step 3.  Generate Minimum Bounding Rectangle by using min max.

bottomleftCorner = new Vector3(minXYZ[0], minXYZ[1], pointarr[0].z);

bottomRightCorner = new Vector3(maxXYZ[0], minXYZ[1], pointarr[0].z);

topLeftCorner = new Vector3(minXYZ[0], maxXYZ[1], pointarr[0].z);

topRightCorner = new Vector3(maxXYZ[0], maxXYZ[1], pointarr[0].z);

Note:- set Z-value of Bounding Rectangle Equal to Rotated Polygon Z Value for Perfect Align. Instead of Min Z and Max Z. 
Step 4. Rotate Computed Bounding rectangle Reverse of Edge Align X-Axis Matrix.

step 5.  rotate Bounding rectangle back to Original polygon direction by using reverse of Rotation matrix.

How to find Bounding Rectangle of 3D Polygon

I have an arbitrary polygon as shown in Pic with co-planar Vertices's A,B,C,D,E,F,G,H in 3 D coordinate System. This Polygon is about to arbitrary axis. 

1.Rotate this arbitrary polygon  in X-Y Axis. 

How to rotate Polygon from arbitrary Axis to X-Y Axis.

Compute normal of given Polygon. lets Assume normal of Polygon is Vector Nsrc.

Normal for any plane in X-Y axis will Z-direction so normal for X-Y Plane Vector Ndst (0,0,1).

By using Nsrc (source normal) and  Ndst(destination Normal) compute rotation matrix and rotate plane in X-Y Axis.

2. Compute Min-Max for Rotated Polygon. i. e minXYZ[] and maxXYZ[] and generate Bounding rectangle by using min max.

bottomleftCorner = new Vector3(minXYZ[0], minXYZ[1], pointarr[0].z);

bottomRightCorner = new Vector3(maxXYZ[0], minXYZ[1], pointarr[0].z);

topLeftCorner = new Vector3(minXYZ[0], maxXYZ[1], pointarr[0].z);

topRightCorner = new Vector3(maxXYZ[0], maxXYZ[1], pointarr[0].z);

Note:- set Z-value of Bounding Rectangle Equal to Rotated Polygon Z Value for Perfect Align. Instead of Min Z and Max Z. 

3.  rotate Bounding rectangle back to Original polygon direction by using reverse of Rotation matrix.

Bounding Rectangle

How to sort 3D vertices of a polygon in order?

we are given multiple random coplanar 3D points. Compute normal by any 3 Point. we need to rotate all these point in X-Y plane. So compute rotation matrix normal to (0,0,1). rotate all these in X-Y plane.

      double[] normal = PlaneUtils.getNormal(tverts);

      Vector3 srcNormal = new Vector3(normal[0], normal[1], normal[2]).normalize();

      Vector3 destNormal = new Vector3(0, 0, 1);

      // Rotation Matrix of Arbitrary Polygon From Current Plane to XY Plane

      Matrix4 rotationMatrix = Matrix4.rotate(destNormal, srcNormal);

      for (int i = 0; i < PointArrVal.length; i++) {

        PointArrVal[i].timesEquals(rotationMatrix);

      }

Now Compute Mean of All X-coordinate and mean of All Y-coordinate.

Mean of X= Sum of All X-coordinate/number of Point and in same way compute mean of Y.

Compute Atan2 angle between Mean Point and given coordinate.

Math.atan2(clipCornerPoint[i].y - cY, clipCornerPoint[i].x - cX), clipCornerPoint[i]

Store computed angle with vertices in Ordered Multi Map like

TreeMap <Double, List<Point3>> multimap = new TreeMap<Double, List<Point3>>();
      for (int i = 0; i < clipCornerPoint.length; i++) {
        putObjects(multimap, Math.atan2(clipCornerPoint[i].y - cY, clipCornerPoint[i].x - cX), clipCornerPoint[i]);
      }

Sort map angle as key and it will give you vertices in order.

now reverse your point in same previous Arbitrary Axis by inverse Rotation Matrix.

A habit of donation “We only have what we give.”

I started my earning(income) journey from Reliance Jio as Software Developer in 10 July 2012 on my b'day. I was happy to join company.because it is very big industry. there was one dream from College time that when  I will earn I will donate some part of my salary every month. I got my first salary in august around 22K. all of my friends and me were happy with first salary and planning to go outside for celebration and I forgot my small dream.One Sunday i was enjoying tea with my friend and i saw a beggar in Mumbai i thought for a moment and my donation dream strike in my mind. but as human nature I started giving excuse to myself  "first make yourself at some level to give donation". why should i give my hard earning money ? Beggar can also earn he also have hand blah.... But I learned one thing that It was very difficult to donate 10rs from your hard earned salary. But in the evening  I opened a Recurring deposit in my salary Account and started to save 2% of my monthly salary that was around 600rs and thus i made yearly saving of 7200rs. I donated this 7200rs  for treatment  of one old cow in my village. Then i got increment next year my salary became 40K so 2% of that was 9600 rs yearly. I bought some sport material and exercising equipments for the sport club of my village. In 3rd year 2% of my salary was 12000rs. I donated to my village Gausala. Then I switched my Job from Reliance to VizExperts Gurgaon. Now 2% of my annual income is Rs 16800. now I am thinking of donating it to a cancer patient in my village. I feel always very happy about this initiative taken by me. it is only 2% of my salary but a good amount to help someone.

“There is nothing more beautiful than someone who goes out of their way to make life beautiful for others.”