Skip to content

Commit

Permalink
Refactored code to make the interpolation methods more general to wor…
Browse files Browse the repository at this point in the history 
…k for all curves
  • Loading branch information
@Habrador
Habrador committed Mar 14, 2020
1 parent 54c020e commit 384980f
Show file tree
Hide file tree
Showing 6 changed files with 396 additions and 166 deletions.
140 changes: 118 additions & 22 deletions Assets/Test scenes/7. Interpolation/InterpolationController.cs
View file
Expand Up @@ -37,20 +37,22 @@ private void OnDrawGizmos()

//BezierQuadratic(posA, posB, handleA);

//BezierQuadraticEqualSteps(posA, posB, handleA);

//BezierCubic(posA, posB, handleA, handleB);

//BezierCubicEqualSteps(posA, posB, handleA, handleB);
BezierCubicEqualSteps(posA, posB, handleA, handleB);

//CatmullRom(posA, handleA, handleB, posB);


//Interpolation between values
OtherInterpolations(posA, posB);
//OtherInterpolations(posA, posB);
}



private void BezierLinear(MyVector3 a, MyVector3 b)
private void BezierLinear(MyVector3 posA, MyVector3 posB)
{
//Store the interpolated values so we later can display them
List<Vector3> interpolatedValues = new List<Vector3>();
Expand All @@ -68,7 +70,7 @@ private void BezierLinear(MyVector3 a, MyVector3 b)
{
//Debug.Log(t);

MyVector3 interpolatedValue = _Interpolation.BezierLinear(a, b, t);
MyVector3 interpolatedValue = _Interpolation.BezierLinear(posA, posB, t);

interpolatedValues.Add(interpolatedValue.ToVector3());

Expand Down Expand Up @@ -129,6 +131,89 @@ private void BezierQuadratic(MyVector3 posA, MyVector3 posB, MyVector3 handle)
Gizmos.DrawWireSphere(slidePos.ToVector3(), 0.15f);
}

private void BezierQuadraticEqualSteps(MyVector3 posA, MyVector3 posB, MyVector3 handle)
{
//Store the interpolated values so we later can display them
List<Vector3> actualPositions = new List<Vector3>();

//Create a curve which is the data structure used in the following calculations
BezierQuadratic bezierQuadratic = new BezierQuadratic(posA, posB, handle);


//Step 1. Calculate the length of the entire curve
//This is needed to so we know how long we should walk each step
float lengthNaive = InterpolationHelpMethods.GetLength_Naive(bezierQuadratic, steps: 20, tEnd: 1f);

float lengthExact = InterpolationHelpMethods.GetLength_SimpsonsRule(bezierQuadratic, tStart: 0f, tEnd: 1f);

Debug.Log("Naive length: " + lengthNaive + " Exact length: " + lengthExact);





int steps = 5;

//Important not to confuse this with the step size we use to iterate t
//This step size is distance in m
float length = lengthNaive;

float lengthStepSize = length / (float)steps;

float stepSize = 1f / (float)steps;

float t = 0f;

float distanceTravelled = 0f;

for (int i = 0; i < steps + 1; i++)
{
//MyVector3 inaccuratePos = bezierCubic.GetInterpolatedValue(t);



//Calculate t to get to this distance
//Method 1
//float actualT = InterpolationHelpMethods.Find_t_FromDistance_Iterative(bezierQuadratic, distanceTravelled, length);
//Method 2
float actualT = InterpolationHelpMethods.Find_t_FromDistance_Lookup(bezierQuadratic, distanceTravelled, accumulatedDistances: null);

MyVector3 actualPos = bezierQuadratic.GetInterpolatedValue(actualT);

actualPositions.Add(actualPos.ToVector3());



//Test that the derivative calculations are working
float dEst = InterpolationHelpMethods.EstimateDerivative(bezierQuadratic, t);
float dAct = bezierQuadratic.ExactDerivative(t);

Debug.Log("Estimated derivative: " + dEst + " Actual derivative: " + dAct);



//Debug.Log("Distance " + distanceTravelled);

//Move on to next iteration
distanceTravelled += lengthStepSize;

t += stepSize;
}

//List<MyVector3> positionsOnCurve = InterpolationHelpMethods.SplitCurve(bezierQuadratic, 20, tEnd: 1f);

//foreach (MyVector3 p in positionsOnCurve)
//{
// Gizmos.DrawWireSphere(p.ToVector3(), 0.1f);
//}

DisplayInterpolatedValues(actualPositions, useRandomColor: true);

//Display the start and end values and the handle points
DisplayHandle(handle.ToVector3(), posA.ToVector3());
DisplayHandle(handle.ToVector3(), posB.ToVector3());
}



private void BezierCubic(MyVector3 posA, MyVector3 posB, MyVector3 handleA, MyVector3 handleB)
Expand Down Expand Up @@ -167,7 +252,9 @@ private void BezierCubic(MyVector3 posA, MyVector3 posB, MyVector3 handleA, MyVe

//Display other related data
//Get the orientation of the point at t
InterpolationTransform trans = _Interpolation.BezierCubicTransform(posA, posB, handleA, handleB, tSliderValue);
BezierCubic bezierCubic = new BezierCubic(posA, posB, handleA, handleB);

InterpolationTransform trans = bezierCubic.GetTransform(tSliderValue);

//Multiply the orientation with a direction vector to rotate the direction
Vector3 forwardDir = trans.Forward.ToVector3();
Expand All @@ -191,14 +278,17 @@ private void BezierCubicEqualSteps(MyVector3 posA, MyVector3 posB, MyVector3 han
//Store the interpolated values so we later can display them
List<Vector3> actualPositions = new List<Vector3>();

//Create a curve which is the data structure used in the following calculations
BezierCubic bezierCubic = new BezierCubic(posA, posB, handleA, handleB);


//Step 1. Calculate the length of the entire curve
//This is needed to so we know how long we should walk each step
//float length = InterpolationHelpMethods.GetLengthNaiveCubicBezier(posA, posB, handleA, handleB, steps: 20, tEnd: 1f);
float lengthNaive = InterpolationHelpMethods.GetLength_Naive(bezierCubic, steps: 20, tEnd: 1f);

float length = InterpolationHelpMethods.GetLengthSimpsonsRule_CubicBezier(posA, posB, handleA, handleB, tStart: 0f, tEnd: 1f);
float lengthExact = InterpolationHelpMethods.GetLength_SimpsonsRule(bezierCubic, tStart: 0f, tEnd: 1f);

//Debug.Log(length + " " + lengthOther);
Debug.Log("Naive length: " + lengthNaive + " Exact length: " + lengthExact);



Expand All @@ -208,6 +298,8 @@ private void BezierCubicEqualSteps(MyVector3 posA, MyVector3 posB, MyVector3 han

//Important not to confuse this with the step size we use to iterate t
//This step size is distance in m
float length = lengthNaive;

float lengthStepSize = length / (float)steps;

float stepSize = 1f / (float)steps;
Expand All @@ -218,35 +310,39 @@ private void BezierCubicEqualSteps(MyVector3 posA, MyVector3 posB, MyVector3 han

for (int i = 0; i < steps + 1; i++)
{
//MyVector3 actualPos = _Interpolation.BezierCubic(posA, posB, handleA, handleB, t);

//Method 1
//float actualT = InterpolationHelpMethods.Find_t_FromDistance_CubicBezier_Iterative(posA, posB, handleA, handleB, distanceTravelled, length);
//MyVector3 inaccuratePos = bezierCubic.GetInterpolatedValue(t);



//Calculate t to get to this distance
//Method 1
//float actualT = InterpolationHelpMethods.Find_t_FromDistance_Iterative(bezierCubic, distanceTravelled, length);
//Method 2
float actualT = InterpolationHelpMethods.Find_t_FromDistance_CubicBezier_Lookup(
posA, posB, handleA, handleB, distanceTravelled, accumulatedDistances: null);
float actualT = InterpolationHelpMethods.Find_t_FromDistance_Lookup(bezierCubic, distanceTravelled, accumulatedDistances: null);

MyVector3 actualPos = _Interpolation.BezierCubic(posA, posB, handleA, handleB, actualT);
MyVector3 actualPos = bezierCubic.GetInterpolatedValue(actualT);

//float dEst = MyVector3.Magnitude(InterpolationHelpMethods.EstimateDerivativeCubicBezier(posA, posB, handleA, handleB, t));
//float dAct = MyVector3.Magnitude(InterpolationHelpMethods.DerivativeCubicBezier(posA, posB, handleA, handleB, t));
actualPositions.Add(actualPos.ToVector3());

//Debug.Log("Estimated derivative: " + dEst + " Actual derivative: " + dAct);

//Debug.Log("Distance " + distanceTravelled);

//MyVector3 actualPos = _Interpolation.BezierCubic(posA, posB, handleA, handleB, actualT);
//Test that the derivative calculations are working
float dEst = InterpolationHelpMethods.EstimateDerivative(bezierCubic, t);
float dAct = bezierCubic.ExactDerivative(t);

Debug.Log("Estimated derivative: " + dEst + " Actual derivative: " + dAct);

actualPositions.Add(actualPos.ToVector3());


//Debug.Log("Distance " + distanceTravelled);

//Move on to next iteration
distanceTravelled += lengthStepSize;

t += stepSize;
}

//List<MyVector3> positionsOnCurve = InterpolationHelpMethods.SplitCurve_CubicBezier(posA, posB, handleA, handleB, 20, tEnd: 1f);
//List<MyVector3> positionsOnCurve = InterpolationHelpMethods.SplitCurve(bezierCubic, 20, tEnd: 1f);

//foreach (MyVector3 p in positionsOnCurve)
//{
Expand Down
6 changes: 3 additions & 3 deletions Assets/Test scenes/7. Interpolation/interpolation.unity
View file
Expand Up @@ -205,7 +205,7 @@ Transform:
m_PrefabAsset: {fileID: 0}
m_GameObject: {fileID: 733677671}
m_LocalRotation: {x: 0, y: 0, z: 0, w: 1}
m_LocalPosition: {x: -2.93, y: 0, z: -2.48}
m_LocalPosition: {x: -4.24, y: 0, z: -2.95}
m_LocalScale: {x: 1, y: 1, z: 1}
m_Children: []
m_Father: {fileID: 0}
Expand Down Expand Up @@ -235,7 +235,7 @@ Transform:
m_PrefabAsset: {fileID: 0}
m_GameObject: {fileID: 759434768}
m_LocalRotation: {x: 0, y: 0, z: 0, w: 1}
m_LocalPosition: {x: 2.83, y: 0, z: -2.28}
m_LocalPosition: {x: 2.5, y: 0, z: -2.2}
m_LocalScale: {x: 1, y: 1, z: 1}
m_Children: []
m_Father: {fileID: 0}
Expand Down Expand Up @@ -343,7 +343,7 @@ Transform:
m_PrefabAsset: {fileID: 0}
m_GameObject: {fileID: 1871846292}
m_LocalRotation: {x: 0, y: 0, z: 0, w: 1}
m_LocalPosition: {x: -3.49, y: 0, z: 0.07}
m_LocalPosition: {x: -4.09, y: 0, z: 2.12}
m_LocalScale: {x: 1, y: 1, z: 1}
m_Children: []
m_Father: {fileID: 0}
Expand Down

0 comments on commit 384980f

Please sign in to comment.