GenerateDemoFiles.cs

using REST_JSON_API;
using System;
using System.Collections.Generic;
using System.Linq;
using Unity.Mathematics;
using UnityEngine;

public class GenerateDemoFiles
{
    public static void GenerateAll()
    {
        if (UnityEngine.Object.FindObjectOfType<GadgetBehaviour>(true) == null)
        {
            Debug.LogError("Cannot GenerateDemoFiles without populated GadgetManager");
            return;
        }

        Debug.LogWarning("Generating and Overwriting Stage Files");

        Action[] DemoGeneration = new Action[]{
            GenerateTreeStage,
            GenerateRiverStage,
            GenerateCanonBallStage2D,
            GenerateCanonBallStage3D,
            GenerateSlingShotStage,
        };

        foreach (Action action in DemoGeneration)
            try
            {
                action();
                Debug.Log("Successfully executed " + action.Method.Name);
            }
            catch (Exception ex)
            {
                Debug.LogError("Exception while executing " + action.Method.Name);
                Debug.LogException(ex);
            }
    }

    public static void GenerateSlingShotStage()
    {
        // SlingShot
        float angle = 45;

        float[,] slingshot = new float[,] {
            {
              -24.32552f,
              1.83532131f,
              1.56619191f
            },
            {
              -24.32552f,
              0.7562289f,
              1.56619227f
            },
            {
              -24.32552f,
              0.7562293f,
              3.46392965f
            },
        };

        // set 
        Vector3 a = new Vector3(slingshot[0, 0], slingshot[0, 1], slingshot[0, 2]);
        Vector3 b = new Vector3(slingshot[1, 0], slingshot[1, 1], slingshot[1, 2]);
        Vector3 c = new Vector3(slingshot[2, 0], slingshot[2, 1], slingshot[2, 2]);

        c = (1 / Mathf.Tan(angle.ToRadians()) * (a - b).magnitude)
          * (c-b).normalized + b;

        slingshot[2, 0] = c.x;
        slingshot[2, 1] = c.y;
        slingshot[2, 2] = c.z;

        // Generate Stage
        StageStatic.LoadNewStage
        (
            id: 3,
            category: "Demo Category",
            name: "SlingShot",
            scene: "RiverWorld",
            description: "Find the correct velocity for the SlingShot to bounce once on the island within range, such that the projectile lands on the other side.",
            local: false,
            forcelocal: true
        );

        //// Populate Solution
        float[,] coords = new float[,] {
            {
               -25.2272873f,
               -0.0546216965f,
               -5.025429f
            },
            {
                -27.42147f,
                -0.008223057f,
                -6.39225769f
            },
            {
                -22.7489357f,
                -0.161126614f,
                -4.983921f
            },
            {
                -23.9606457f,
                -0.0313406f,
                -6.32592f
            },
            {
                -24.1699982f,
                -0.0106577873f,
                -4.862953f
            },
            {
                -29.479023f,
                -0.00494384766f,
                -8.160179f
            },
            {
                -22.68462f,
                -0.00494480133f,
                -9.776779f
            },
            {
                -20.088747f,
                -0.00494384766f,
                -8.493519f
            },
            {
                -33.77201f,
                -0.00494432449f,
                -9.721775f
            },
            {
                -39.13363f,
                -0.00494432449f,
                -9.173346f
            },
            {
                -5.162197f,
                -0.01788807f,
                -10.8270531f
            },
            {
                -2.14803314f,
                -0.00494384766f,
                -12.0348969f
            },
            {
                3.33150864f,
                -0.00494432449f,
                -15.5597382f
            },
            {
                5.57119f,
                -0.00609874725f,
                -16.0912876f
            },
            {
                7.786186f,
                -0.00494480133f,
                -15.6361771f
            },
            {
                12.9067154f,
                -0.02451706f,
                -12.6005821f
            },
            {
                13.9139938f,
                -0.00585222244f,
                -12.8295422f
            },
            {
                14.9375687f,
                -0.00494432449f,
                -13.4600468f
            },
            {
                18.0826569f,
                -0.00494432449f,
                -14.8706532f
            },
            {
                20.7500458f,
                -0.00614357f,
                -14.5210171f
            },
            {
                23.5185432f,
                -0.00494432449f,
                -12.6296406f
            },
            {
                26.0413818f,
                -0.00494432449f,
                -10.1295071f
            },
            {
                33.0014877f,
                -0.00494384766f,
                -11.9421864f
            },
            {
                38.6853943f,
                -0.0156846046f,
                -16.7288418f
            },
            {
                38.2561569f,
                -0.00494432449f,
                -38.421936f
            },
            {
                -36.2956123f,
                -0.00494432449f,
                -39.43577f
            },
            {
                -38.7866669f,
                -0.00494432449f,
                39.2549057f
            },
            {
                39.66716f,
                -0.00494432449f,
                39.7287445f
            },
        };

        List<string> PIds = new();
        List<Vector3> verts = new();
        bool samestep = false;
        for (int i = 0; i < coords.GetLength(0); i++)
        {
            verts.Add(new Vector3(coords[i, 0], coords[i, 1], coords[i, 2]));

            PIds.Add(
                StageStatic.stage.solution.Add(
                    new PointFact(verts.Last(), Vector3.up),
                    out _, samestep, null, null, true
            ));
            //StageStatic.stage.solution.ExposedSolutionFacts.Add(PIds.Last());
            samestep = true;
        }

        // island
        List<TriangleFact> Tris = new List<TriangleFact>();
        Tris.Add(new TriangleFact(new Vector3[] { verts[0], verts[3], verts[1] }));
        Tris.Add(new TriangleFact(new Vector3[] { verts[0], verts[4], verts[3] }));
        Tris.Add(new TriangleFact(new Vector3[] { verts[4], verts[2], verts[3] }));

        // landing Zone
        Vector3[] plane = verts
            .GetRange(5, verts.Count - 5 - 3)
            .OrderBy(v => Vector3.Dot(-Vector3.right, (v - verts[^3]).normalized))
            .ToArray();

        for (int i = 0; i < plane.Length-1; i++)
            Tris.Add(new TriangleFact(new Vector3[] { verts[^3], plane[i], plane[i + 1] }));

        // bottom
        Vector3 offset_bottom = new Vector3(0, -2, 0);
        Tris.Add(new TriangleFact(new Vector3[] { verts[^1], verts[^2], verts[^3] }.Select(v => v + offset_bottom).ToArray()));
        Tris.Add(new TriangleFact(new Vector3[] { verts[^1], verts[^3], verts[^4] }.Select(v => v + offset_bottom).ToArray()));

        // cleanup
        List<string> TrisID = new();
        for (int i = 0; i < Tris.Count; i++)
        {
            TrisID.Add(
                StageStatic.stage.solution.Add(Tris[i], out _, samestep, null, null, true)
            );
            //StageStatic.stage.solution.ExposedSolutionFacts.Add(TrisID.Last());
        }

        string TriangleURI = StageStatic.stage.solution.Add( // for CannonBallScroll
            new ListFact(TrisID.ToArray(), null, new OMS(MMTConstants.TYPE_TO_OMS[typeof(TriangleFact)])),
            out bool _, true, null, null, true
        );
        //StageStatic.stage.solution.ExposedSolutionFacts.Add(TriangleURI);

        string GravURI = StageStatic.stage.solution.Add(
            new PointFact(new Vector3(0, -9.81f, 0), Vector3.down),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(GravURI);

        string BounceURI = StageStatic.stage.solution.Add(
            new RealLitFact(0.8f),
            out _, false, null, null);
        //StageStatic.stage.solution.ExposedSolutionFacts.Add(BounceURI);

        // insert slingshot
        for (int i = 0; i < slingshot.GetLength(0); i++)
        {
            verts.Add(new Vector3(slingshot[i, 0], slingshot[i, 1], slingshot[i, 2]));

            PIds.Add(
                StageStatic.stage.solution.Add(
                    new PointFact(verts.Last(), Vector3.up),
                    out _, samestep, null, null, true
            ));
            StageStatic.stage.solution.ExposedSolutionFacts.Add(PIds.Last());
            samestep = true;
        }

        //// Set Solution
        //StageStatic.stage.solution.ValidationSet =
        //    new List<SolutionRecorder.SubSolution>
        //    { new SolutionRecorder.SubSolution(new HashSet<string> { target_Id }, null, null, new LineFactHightDirectionComparer()) };

        // Set Gadgets/ Scrolls
        StageStatic.stage.AllowedGadgets = null;
        StageStatic.stage.AllowedScrolls = new() { MMTConstants.ScrollRiverSimple, MMTConstants.ScrollRiver, MMTConstants.ScrollCannonBallT3D };

        StageStatic.stage.solution.ScrollOverwrites.Add(MMTConstants.ScrollCannonBallT3D, new[] {
            (GravURI, 2, false),
            (BounceURI, 3, false),
            (TriangleURI, 4, false),
        });
        StageStatic.stage.solution.ScrollOverwrites.Add(MMTConstants.ScrollRiver, new[] {
            (GravURI, 4, false),
        });
        StageStatic.stage.solution.ScrollOverwrites.Add(MMTConstants.ScrollRiverSimple, new[] {
            (GravURI, 2, true),
        });

        // Save
        StageStatic.SetMode(StageStatic.Mode.Create);
        StageStatic.stage.store(false, true);
    }

    public static void GenerateTreeStage()
    {
        // Params
        float minimalSolutionHight = 6;

        // Generate Stage
        StageStatic.LoadNewStage
        (
            id: 1,
            category: "Demo Category",
            name: "TechDemo A",
            scene: "RiverWorld",
            description: "Tree Stage",
            local: false,
            forcelocal: true
        );

        // Populate Solution
        PointFact
            buttom = new PointFact(Vector3.zero, Vector3.up),
            top = new PointFact(Vector3.zero + Vector3.up * minimalSolutionHight, Vector3.up);

        StageStatic.stage.solution.Add(buttom, out _, false, null, null);
        StageStatic.stage.solution.Add(top, out _, true, null, null);

        LineFact target = new LineFact(buttom.Id, top.Id);
        var target_Id = StageStatic.stage.solution.Add(target, out _, true, null, null);

        // Set Solution
        StageStatic.stage.solution.ValidationSet =
            new List<SolutionRecorder.SubSolution>
            { new SolutionRecorder.SubSolution(new HashSet<string> { target_Id }, null, null, new LineFactHightDirectionComparer()) };

        // Set Gadgets/ Scrolls
        StageStatic.stage.AllowedGadgets = null;
        StageStatic.stage.AllowedScrolls = null;

        // Save
        StageStatic.SetMode(StageStatic.Mode.Create);
        StageStatic.stage.store(false, true);
    }

    public static void GenerateRiverStage()
    {
        // Params
        float minimalSolutionHight = 6;

        // Generate Stage
        StageStatic.LoadNewStage
        (
            id: 2,
            category: "Demo Category",
            name: "TechDemo B",
            scene: "RiverWorld",
            description: "River Stage",
            local: false,
            forcelocal: true
        );

        // Populate Solution
        PointFact
            buttom = new PointFact(Vector3.zero, Vector3.up),
            top = new PointFact(Vector3.zero + Vector3.up * minimalSolutionHight, Vector3.up);

        StageStatic.stage.solution.Add(buttom, out _, false, null, null);
        StageStatic.stage.solution.Add(top, out _, true, null, null);

        LineFact target = new LineFact(buttom.Id, top.Id);
        var target_Id = StageStatic.stage.solution.Add(target, out _, true, null, null);

        // Set Solution
        StageStatic.stage.solution.ValidationSet =
            new List<SolutionRecorder.SubSolution> {
                new SolutionRecorder.SubSolution(new HashSet<string> { target_Id }, null, null, new LineFactHightDirectionComparer()),
                new SolutionRecorder.SubSolution(new HashSet<string> { target_Id }, null, null, new LineSpanningOverRiverWorldComparer()),
                new SolutionRecorder.SubSolution(null, new List<int> { 1 }, new List<int> { 0 }, new LineFactHightComparer()),
            };

        // Set Gadgets/ Scrolls
        StageStatic.stage.AllowedGadgets = new() { new Pointer(), new Tape(), new AngleTool(), new LineTool(), new LotTool(), new Pendulum(), new Remover() }; //, new EqualCircleGadget(), new TestMiddlePoint() };
        StageStatic.stage.AllowedScrolls = new() {
            "http://mathhub.info/FrameIT/frameworld?OppositeLen",
            //"http://mathhub.info/FrameIT/frameworld?SupplementaryAngles",
            //"http://mathhub.info/FrameIT/frameworld?AngleSum",
            //"http://mathhub.info/FrameIT/frameworld?Pythagoras",
            //"http://mathhub.info/FrameIT/frameworld?CylinderVolumeScroll",
            //"http://mathhub.info/FrameIT/frameworld?CircleLineAngleToAngleScroll",
            //"http://mathhub.info/FrameIT/frameworld?Midpoint",
            //"http://mathhub.info/FrameIT/frameworld?CircleScroll",
            //"http://mathhub.info/FrameIT/frameworld?CircleLineAngleScroll",
            //"http://mathhub.info/FrameIT/frameworld?CircleAreaScroll",
            //"http://mathhub.info/FrameIT/frameworld?ConeVolumeScroll",
            //"http://mathhub.info/FrameIT/frameworld?TruncatedConeVolumeScroll",
        };

        // Save
        StageStatic.SetMode(StageStatic.Mode.Create);
        StageStatic.stage.store(false, true);
    }

    public static void GenerateCanonBallStage2D()
    {
        // Params //List<Wall> walls, T starPos, T starVec, T gravity, int dimension
        int
            dim_const = 0,
            dim_A = 1,
            dim_B = 2;

        float Py_factor = 0.04905f;
        float Py_bounce = 0.8f;

        float3 StartPos_py = new(0.0f, 300.0f, 380.0f);
        float3 StartVec_py = new(0.0f, 150.0f, -490.0f);
        float3 Gravity_py = new(0.0f, -200f, 0.0f);

        (double x1, double x2, double y1, double y2)[] PythonParams = {
            (-1.0, 0.0, 401.0, 0.0 ),
            (0.0, -1.0, 0.01, 401.0 ),
            (400.0, -1.0, 400.01, 401.0),
            (-1.0, 400.0, 401.0, 400.0),
            (50.0, 200.0, 120.0, 270.0),
            (150.0, 100.0, 200.0, 100.0),
            (150.0, 285.0, 200.0, 200.0),
            (230.0, 360.0, 300.0, 300.0),
            (300.0, 100.0, 385.0, 150.0),
            (50.0, 50.0, 100.0, 135.0),
        };

        //Parse PythonParams
        Vector3
            StartPos = Vector3.zero,
            StartVec = Vector3.zero,
            Gravity = Vector3.zero;


        StartPos[0] = StartPos_py[0] * Py_factor;
        StartPos[1] = StartPos_py[1] * Py_factor;
        StartPos[2] = StartPos_py[2] * Py_factor;

        StartVec[0] = StartVec_py[0] * Py_factor;
        StartVec[1] = StartVec_py[1] * Py_factor;
        StartVec[2] = StartVec_py[2] * Py_factor;

        Gravity[0] = Gravity_py[0] * Py_factor;
        Gravity[1] = Gravity_py[1] * Py_factor;
        Gravity[2] = Gravity_py[2] * Py_factor;

        float[,,] Wall_parameter = new float[PythonParams.Length, 2, 2];
        for (uint i = 0; i < PythonParams.Length; i++)
        {
            Wall_parameter[i, 0, 0] = (float)(Py_factor * (PythonParams[i].x1));
            Wall_parameter[i, 0, 1] = (float)(Py_factor * (PythonParams[i].x2));

            Wall_parameter[i, 1, 0] = (float)(Py_factor * (PythonParams[i].y1));
            Wall_parameter[i, 1, 1] = (float)(Py_factor * (PythonParams[i].y2));
        }

        // Generate Stage
        StageStatic.LoadNewStage
        (
            id: 1,
            category: "CanonBall",
            name: "CanonBall 2D",
            scene: "RiverWorld",
            description: "CanonBall 2D Test",
            local: false,
            forcelocal: true
        );

        // Populate Solution

        string BallURI = StageStatic.stage.solution.Add(
            new PointFact(StartPos, Vector3.up),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(BallURI);

        string VecURI = StageStatic.stage.solution.Add(
            new PointFact(StartVec, StartVec.normalized),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(VecURI);

        string GravURI = StageStatic.stage.solution.Add(
            new PointFact(Gravity, Gravity.normalized),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(GravURI);

        string BounceURI = StageStatic.stage.solution.Add(
            new RealLitFact(Py_bounce),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(BounceURI);

        List<LineFact> Walls = new();
        for (int i = 0; i < PythonParams.Length; i++)
        {
            Vector3 tmpVec = Vector3.zero;

            tmpVec[dim_A] = Wall_parameter[i, 0, 1];
            tmpVec[dim_B] = Wall_parameter[i, 0, 0];
            PointFact topA = new(tmpVec, Vector3.up);
            string topAURI = StageStatic.stage.solution.Add(topA, out _, false, null, null);

            tmpVec[dim_A] = Wall_parameter[i, 1, 1];
            tmpVec[dim_B] = Wall_parameter[i, 1, 0];
            PointFact topB = new(tmpVec, Vector3.up);
            string topBURI = StageStatic.stage.solution.Add(topB, out _, true, null, null);

            LineFact topology = new(topAURI, topBURI);
            string lineURI = StageStatic.stage.solution.Add(topology, out _, true, null, null);
            StageStatic.stage.solution.ExposedSolutionFacts.Add(lineURI);

            Walls.Add(topology);
        }

        // Set Solution
        #region  CannonBallScroll
        //StageStatic.stage.solution.Add( // for CannonBallScroll
        //    new ListFact(Walls.Select(w => w.Topology.Id).ToArray(), null, new OMS(MMTConstants.TYPE_TO_OMS[typeof(LineFact)]), StageStatic.stage.solution),
        //    out bool _, true, null, null
        //);

        // special case for Prototype
        SOMDoc[] RRRRTupel = new SOMDoc[Walls.Count];
        for (int i = 0; i < Walls.Count; i++)
        {
            RRRRTupel[i] =
                SOMDoc.MakeTupel(
                    new[] {
                        SOMDoc.MakeTupel(new OMLIT<float>[] { new((float)PythonParams[i].x1), new((float)PythonParams[i].x2) }),
                        SOMDoc.MakeTupel(new OMLIT<float>[] { new((float)PythonParams[i].y1), new((float)PythonParams[i].y2) }),
                });
        }
        string RRRRURI = StageStatic.stage.solution.Add(
            new ListFact(null, RRRRTupel, null),
            out bool _, true, null, null
        );
        #endregion CannonBallScroll

        CanonBallProblemCalculator2D calc = new(Walls, StartPos, StartVec, Gravity, Py_bounce, dim_const, dim_A, dim_B, StageStatic.stage.solution);
        StageStatic.stage.solution.ExposedSolutionFacts.AddRange(calc.Result_FuncCall_Id);

        //string attacheFactURI = StageStatic.stage.solution.Add(
        //    new AttachedPositionFunction(BallURI, calc.Result_FuncCall_Id.ToArray(), StageStatic.stage.solution),
        //    out _, true, null, null);
        //StageStatic.stage.solution.ExposedSolutionFacts.Add(attacheFactURI);

        //TODO: ~attach funcs + ~cheat?
        //StageStatic.stage.solution.ValidationSet =
        //        new List<SolutionOrganizer.SubSolution> {
        //        new SolutionOrganizer.SubSolution(new HashSet<string> { target_Id }, null, null, new LineFactHightDirectionComparer()),
        //        new SolutionOrganizer.SubSolution(new HashSet<string> { target_Id }, null, null, new LineSpanningOverRiverWorldComparer()),
        //        new SolutionOrganizer.SubSolution(null, new List<int> { 1 }, new List<int> { 0 }, new LineFactHightComparer()),
        //        };

        // Set Gadgets/ Scrolls
        StageStatic.stage.AllowedGadgets = null;
        StageStatic.stage.AllowedScrolls = new() { MMTConstants.ScrollCannonBall2D };
        StageStatic.stage.solution.ScrollOverwrites.Add(MMTConstants.ScrollCannonBall2D, new[] {
            (BallURI, 0, true),
            (VecURI, 1, true),
            (GravURI, 2, true),
            (BounceURI, 3, true),
            (RRRRURI, 4, true),
        });

        // Save
        StageStatic.SetMode(StageStatic.Mode.Create);
        StageStatic.stage.store(false, true);
    }

    public static void GenerateCanonBallStage3D()
    {
        // Params //List<Wall> walls, T starPos, T starVec, T gravity, int dimension
        int
            dim_G = 1,
            dim_A = 2,
            dim_B = 0;

        float Py_factor = 0.04905f;
        float Py_bounce = 0.8f;

        float3 StartPos_py = new(380, 0, 300);
        float3 StartVec_py = new(-490, 100, 150);
        float3 Gravity_py = new(0, 0, -200);

        double[,,] PythonWalls = new double[,,] {
            {
                { 0, 0, 0 },
                { 400, 0, 0 },
                { 400, 0, 400 },
                { 0, 0, 400 },
            },{
                { 0, 400, 0 },
                { 400, 400, 0 },
                { 400, 400, 400 },
                { 0, 400, 400 },
            },{
                { 250, 0, 0 },
                { 300, 0, 0 },
                { 300, 400, 0 },
                { 250, 400, 0 },
            },{
                { 0, 0, 0 },
                { 0, 0, 400 },
                { 0, 400, 400 },
                { 0, 400, 0 },
            },{
                { 400, 0, 0 },
                { 400, 0, 400 },
                { 400, 400, 400 },
                { 400, 400, 0 },
            },{
                { 0, 0, 400 },
                { 400, 0, 400 },
                { 400, 400, 400 },
                { 0, 400, 400 },
            },{
                { 300, 0, 0 },
                { 400, 0, 0 },
                { 400, 400, 0},
                { 300, 400, 0},
            },{
                { 0, 0, 0 },
                { 250, 0, 0 },
                { 250, 400, 0 },
                { 0, 400, 0 },
            },{
                { 50, 0, 200 },
                { 120.7, 0, 270.7 },
                { 120.7, 200, 270.7 },
                { 50, 200, 200 },
            },{
                { 150, 0, 100 },
                { 200, 0, 100 },
                { 200, 200, 100 },
                { 150, 200, 100 },
            },{
                { 150, 0, 286.6 },
                { 200, 0, 200 },
                { 200, 200, 200 },
                { 150, 200, 286.6 },
            },{
                { 230.7, 0, 340 },
                { 300, 0, 300 },
                { 300, 200, 300 },
                { 230.7, 200, 340 },
            },{
                { 300, 0, 100 },
                { 386.6, 0, 150 },
                { 386.6, 200, 150 },
                { 300, 200, 100 },
            },{
                { 50, 0, 50 },
                { 100, 0, 136.6 },
                { 100, 200, 136.6 },
                { 50, 200, 50 },
        }};

        //Parse PythonParams
        Vector3
            StartPos = Vector3.zero,
            StartVec = Vector3.zero,
            Gravity = Vector3.zero;

        StartPos[dim_A] = StartPos_py[0] * Py_factor;
        StartPos[dim_B] = StartPos_py[1] * Py_factor;
        StartPos[dim_G] = StartPos_py[2] * Py_factor;

        StartVec[dim_A] = StartVec_py[0] * Py_factor;
        StartVec[dim_B] = StartVec_py[1] * Py_factor;
        StartVec[dim_G] = StartVec_py[2] * Py_factor;

        Gravity[dim_A] = Gravity_py[0] * Py_factor;
        Gravity[dim_B] = Gravity_py[1] * Py_factor;
        Gravity[dim_G] = Gravity_py[2] * Py_factor;

        float[,,] Wall_parameter = new float[PythonWalls.GetLength(0), PythonWalls.GetLength(1), PythonWalls.GetLength(2)];
        for (int i = 0; i < PythonWalls.GetLength(0); i++)
            for (int j = 0; j < PythonWalls.GetLength(1); j++)
                for (int k = 0; k < PythonWalls.GetLength(2); k++)
                    Wall_parameter[i, j, k] = (float)(PythonWalls[i, j, k] * Py_factor);

        // Generate Stage
        StageStatic.LoadNewStage
        (
            id: 2,
            category: "CanonBall",
            name: "CanonBall 3D",
            scene: "RiverWorld",
            description: "CanonBall 3D Test",
            local: false,
            forcelocal: true
        );

        // Populate Solution

        string BallURI = StageStatic.stage.solution.Add(
            new PointFact(StartPos, Vector3.up),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(BallURI);

        string VecURI = StageStatic.stage.solution.Add(
            new PointFact(StartVec, StartVec.normalized),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(VecURI);

        string GravURI = StageStatic.stage.solution.Add(
            new PointFact(Gravity, Gravity.normalized),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(GravURI);

        string BounceURI = StageStatic.stage.solution.Add(
            new RealLitFact(Py_bounce),
            out _, false, null, null);
        StageStatic.stage.solution.ExposedSolutionFacts.Add(BounceURI);

        List<QuadFact> Walls = new();
        List<TriangleFact> Trieangles = new();
        for (int i = 0; i < Wall_parameter.GetLength(0); i++)
        {
            Vector3[] corners = new Vector3[4];
            string[] edge = new string[4];

            for (int j = 0; j < Wall_parameter.GetLength(1); j++)
            {
                Vector3 tmpVec = Vector3.zero;
                tmpVec[dim_A] = Wall_parameter[i, j, 0];
                tmpVec[dim_B] = Wall_parameter[i, j, 1];
                tmpVec[dim_G] = Wall_parameter[i, j, 2];
                corners[j] = tmpVec;

                PointFact edge_point = new(tmpVec, Vector3.up);
                edge[j] = StageStatic.stage.solution.Add(edge_point, out _, false, null, null);
            }

            QuadFact topology = new(edge);
            string quadURI = StageStatic.stage.solution.Add(topology, out _, true, null, null);
            StageStatic.stage.solution.ExposedSolutionFacts.Add(quadURI);

            TriangleFact top0 = new(new[] { corners[0], corners[1], corners[2] });
            string top0URI = StageStatic.stage.solution.Add(top0, out _, true, null, null);
            StageStatic.stage.solution.ExposedSolutionFacts.Add(top0URI);

            TriangleFact top1 = new(new[] { corners[2], corners[3], corners[0] });
            string top1URI = StageStatic.stage.solution.Add(top1, out _, true, null, null);
            StageStatic.stage.solution.ExposedSolutionFacts.Add(top1URI);

            Walls.Add(topology);
            Trieangles.Add(top0);
            Trieangles.Add(top1);
        }

        // Set Solution
        #region  CannonBallScroll
        string TriangleURI = StageStatic.stage.solution.Add( // for CannonBallScroll
            new ListFact(Trieangles.Select(q => q.Id).ToArray(), null, new OMS(MMTConstants.TYPE_TO_OMS[typeof(TriangleFact)])),
            out bool _, true, null, null
        );

        // special case for Prototype
        SOMDoc[] RRRRTupel = new SOMDoc[Walls.Count];
        for (int i = 0; i < Walls.Count; i++)
        {
            RRRRTupel[i] = SOMDoc.MakeTupel(
                Walls[i].Pids.Select(p => new OMS(p)).ToArray()
            );
        }
        string QuadURI = StageStatic.stage.solution.Add(
            new ListFact(null, RRRRTupel, null),
            out bool _, true, null, null
        );
        #endregion CannonBallScroll

        CanonBallProblemCalculator3D calc = new(Walls, StartPos, StartVec, Gravity, Py_bounce, dim_G, dim_A, dim_B, StageStatic.stage.solution);
        StageStatic.stage.solution.ExposedSolutionFacts.AddRange(calc.Result_FuncCall_Id);

        //StageStatic.stage.solution.Add( // for reference
        //    new ListFact(calc.Result_FuncCall_Id.ToArray(), null, new OMS("Tuple((txt)x(t->t^)x(t^->fact))"), StageStatic.stage.solution),
        //    out bool _, true, null, null
        //);

        //string attacheFactURI = StageStatic.stage.solution.Add(
        //    new AttachedPositionFunction(BallURI, calc.Result_FuncCall_Id.ToArray(), StageStatic.stage.solution),
        //    out _, true, null, null);
        //StageStatic.stage.solution.ExposedSolutionFacts.Add(attacheFactURI);

        //TODO: ~attach funcs + ~cheat?
        //StageStatic.stage.solution.ValidationSet =
        //        new List<SolutionOrganizer.SubSolution> {
        //        new SolutionOrganizer.SubSolution(new HashSet<string> { target_Id }, null, null, new LineFactHightDirectionComparer()),
        //        new SolutionOrganizer.SubSolution(new HashSet<string> { target_Id }, null, null, new LineSpanningOverRiverWorldComparer()),
        //        new SolutionOrganizer.SubSolution(null, new List<int> { 1 }, new List<int> { 0 }, new LineFactHightComparer()),
        //        };

        // Set Gadgets/ Scrolls
        StageStatic.stage.AllowedGadgets = null;
        StageStatic.stage.AllowedScrolls = new() { MMTConstants.ScrollCannonBall3D, MMTConstants.ScrollCannonBallT3D };
        StageStatic.stage.solution.ScrollOverwrites.Add(MMTConstants.ScrollCannonBall3D, new[] {
            (BallURI, 0, true),
            (VecURI, 1, true),
            (GravURI, 2, true),
            (BounceURI, 3, true),
            (QuadURI, 4, true),
        });
        StageStatic.stage.solution.ScrollOverwrites.Add(MMTConstants.ScrollCannonBallT3D, new[] {
            (BallURI, 0, true),
            (VecURI, 1, true),
            (GravURI, 2, true),
            (BounceURI, 3, true),
            (TriangleURI, 4, true),
        });

        // Save
        StageStatic.SetMode(StageStatic.Mode.Create);
        StageStatic.stage.store(false, true);
    }
}