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using UnityEngine;
using static UnityEngine.Mathf;
public static class FunctionLibrary
{
public delegate Vector3 Function(float u, float v, float y);
public enum FunctionName { Wave, MultiWave, Ripple, Sphere, Torus }
private static Function[] functions = { Wave, MultiWave, Ripple, Sphere, Torus };
public static Function GetFunction(FunctionName name)
{
return functions[(int)name];
}
public static Vector3 Wave(float u, float v, float t)
{
Vector3 p;
p.x = u;
p.y = Sin(PI * (u + v + t));
p.z = v;
return p;
}
public static Vector3 MultiWave(float u, float v, float t)
{
Vector3 p;
p.x = u;
p.y = Sin(PI * (u + 0.5f * t));
p.y += 0.5f * Sin(2f * PI * (v + t));
p.y += Sin(PI * (u + v + 0.25f * t));
p.y *= 1f / 2.5f;
p.z = v;
return p;
}
public static Vector3 Ripple(float u, float v, float t)
{
var d = Sqrt(u * u + v * v);
Vector3 p;
p.x = u;
p.y = Sin(PI * (4f * d - t));
p.y /= 1f + 10f * d;
p.z = v;
return p;
}
public static Vector3 Sphere(float u, float v, float t)
{
float r = 0.9f + 0.1f * Sin(PI * (6f * u + 4f * v + t));
float s = r * Cos(0.5f * PI * v);
Vector3 p;
p.x = s * Sin(PI * u);
p.y = r * Sin(0.5f * PI * v);
p.z = s * Cos(PI * u);
return p;
}
public static Vector3 Torus(float u, float v, float t)
{
float r1 = 0.7f + 0.1f * Sin(PI * (6f * u + 0.5f * t));
float r2 = 0.15f + 0.05f * Sin(PI * (8f * u + 4f * v + 2f * t));
float s = r1 + r2 * Cos(PI * v);
Vector3 p;
p.x = s * Sin(PI * u);
p.y = r2 * Sin(PI * v);
p.z = s * Cos(PI * u);
return p;
}
}

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using UnityEngine;
public class Graph : MonoBehaviour
{
[SerializeField]
Transform pointPrefab = default;
[SerializeField, Range(10, 100)]
int resolution = 10;
[SerializeField]
FunctionLibrary.FunctionName function = default;
Transform[] points;
private void Awake()
{
var step = 2f / resolution;
var scale = Vector3.one * step;
points = new Transform[resolution * resolution];
for (int i = 0; i < points.Length; i++)
{
Transform point = Instantiate(pointPrefab);
point.localScale = scale;
point.SetParent(transform, false);
points[i] = point;
}
}
private void Update()
{
FunctionLibrary.Function f = FunctionLibrary.GetFunction(function);
var time = Time.time;
var step = 2.0f / resolution;
var v = 0.5f * step - 1f;
for (int i = 0, x = 0, z = 0; i < points.Length; i++, x++)
{
if (x == resolution)
{
x = 0;
z += 1;
v = (z + 0.5f) * step - 1f;
}
float u = (x + 0.5f) * step - 1f;
points[i].localPosition = f(u, v, time);
}
}
}

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using UnityEngine;
public class MovingSphere : MonoBehaviour
{
[SerializeField, Range(0f, 100f)]
private float maxSpeed = 10f;
[SerializeField, Range(0f, 100f)]
private float maxAcceleration = 10f, maxAirAcceleration = 1f;
[SerializeField, Range(0f, 10f)]
private float jumpHeight = 2f;
[SerializeField, Range(0, 5)]
private int maxAirJumps = 0;
[SerializeField, Range(0f, 90f)]
private float maxGroundAngle = 25f, maxStairsAngle = 50f;
[SerializeField, Range(0f, 100f)]
float maxSnapSpeed = 100f;
[SerializeField, Min(0f)]
float probeDistance = 1f;
[SerializeField]
LayerMask probeMask = -1, stairsMask = -1;
private Rigidbody body;
private Vector3 desiredVelocity = new Vector3(0f, 0f, 0f);
private bool desiredJump = false;
private int jumpPhase;
private Vector3 velocity;
private Vector3 contactNormal, steepNormal;
private int groundContactCount, steepContactCount;
private float minGroundDotProduct, minStairsDotProduct;
private int stepsSinceLastGrounded, stepsSinceLastJump;
private bool onGround => groundContactCount > 0;
private bool onSteep => steepContactCount > 0;
private float GetMinDot(int layer)
{
return (stairsMask & (1 << layer)) == 0 ?
minGroundDotProduct : minStairsDotProduct;
}
private void OnValidate()
{
minGroundDotProduct = Mathf.Cos(maxGroundAngle * Mathf.Deg2Rad);
minStairsDotProduct = Mathf.Cos(maxStairsAngle * Mathf.Deg2Rad);
}
private void Awake()
{
body = GetComponent<Rigidbody>();
OnValidate();
}
private void Update()
{
Vector2 playerInput;
playerInput.x = Input.GetAxis("Horizontal");
playerInput.y = Input.GetAxis("Vertical");
playerInput = Vector2.ClampMagnitude(playerInput, 1f);
desiredVelocity = new Vector3(playerInput.x, 0f, playerInput.y) * maxSpeed;
desiredJump |= Input.GetButtonDown("Jump");
GetComponent<MeshRenderer>().material.SetColor(
"_BaseColor", onGround ? Color.black : Color.white
);
}
private void FixedUpdate()
{
UpdateState();
AdjustVelocity();
if (desiredJump)
{
desiredJump = false;
Jump();
}
body.velocity = velocity;
ClearState();
}
private void UpdateState()
{
stepsSinceLastGrounded++;
stepsSinceLastJump++;
velocity = body.velocity;
if (onGround || SnapToGround() || CheckSteepContacts())
{
stepsSinceLastGrounded = 0;
if (stepsSinceLastJump > 1)
{
jumpPhase = 0;
}
if (groundContactCount > 1)
{
contactNormal.Normalize();
}
}
else
{
contactNormal = Vector3.up;
}
}
private void OnCollisionEnter(Collision collision)
{
EvaluateCollision(collision);
}
private void OnCollisionStay(Collision collision)
{
EvaluateCollision(collision);
}
private void EvaluateCollision(Collision collision)
{
float minDot = GetMinDot(collision.gameObject.layer);
for (int i = 0; i < collision.contactCount; i++)
{
var normal = collision.GetContact(i).normal;
if (normal.y >= minDot)
{
groundContactCount += 1;
contactNormal += normal;
}
else if (normal.y > -0.01f)
{
steepContactCount += 1;
steepNormal += normal;
}
}
}
private void Jump()
{
Vector3 jumpDirection;
if (onGround)
{
jumpDirection = contactNormal;
}
else if (onSteep)
{
jumpDirection = steepNormal;
jumpPhase = 0;
}
else if (maxAirJumps > 0 && jumpPhase <= maxAirJumps)
{
if (jumpPhase == 0)
{
jumpPhase = 1;
}
jumpDirection = contactNormal;
}
else
{
return;
}
stepsSinceLastJump = 0;
jumpPhase++;
float jumpSpeed = Mathf.Sqrt(-2f * Physics.gravity.y * jumpHeight);
jumpDirection = (jumpDirection + Vector3.up).normalized;
float alignedSpeed = Vector3.Dot(velocity, jumpDirection);
if (alignedSpeed > 0f)
{
jumpSpeed = Mathf.Max(jumpSpeed - alignedSpeed, 0f);
}
velocity += jumpDirection * jumpSpeed;
}
private void AdjustVelocity()
{
Vector3 xAxis = ProjectOnContactPlane(Vector3.right).normalized;
Vector3 zAxis = ProjectOnContactPlane(Vector3.forward).normalized;
float currentX = Vector3.Dot(velocity, xAxis);
float currentZ = Vector3.Dot(velocity, zAxis);
float acceleration = onGround ? maxAcceleration : maxAirAcceleration;
float maxSpeedChange = acceleration * Time.deltaTime;
float newX =
Mathf.MoveTowards(currentX, desiredVelocity.x, maxSpeedChange);
float newZ =
Mathf.MoveTowards(currentZ, desiredVelocity.z, maxSpeedChange);
velocity += xAxis * (newX - currentX) + zAxis * (newZ - currentZ);
}
private Vector3 ProjectOnContactPlane(Vector3 vector)
{
return vector - contactNormal * Vector3.Dot(vector, contactNormal);
}
private void ClearState()
{
groundContactCount = steepContactCount = 0;
contactNormal = steepNormal = Vector3.zero;
}
private bool SnapToGround()
{
if (stepsSinceLastGrounded > 1 || stepsSinceLastJump <= 2)
{
return false;
}
float speed = velocity.magnitude;
if (speed > maxSnapSpeed)
{
return false;
}
if (!Physics.Raycast(body.position, Vector3.down, out RaycastHit hit, probeDistance, probeMask))
{
return false;
}
if (hit.normal.y < GetMinDot(hit.collider.gameObject.layer))
{
return false;
}
groundContactCount = 1;
contactNormal = hit.normal;
float dot = Vector3.Dot(velocity, hit.normal);
if (dot > 0f)
{
velocity = (velocity - hit.normal * dot).normalized * speed;
}
return true;
}
bool CheckSteepContacts()
{
if (steepContactCount > 1)
{
steepNormal.Normalize();
if (steepNormal.y >= minGroundDotProduct)
{
groundContactCount = 1;
contactNormal = steepNormal;
return true;
}
}
return false;
}
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m_LayerCollisionMatrix: fffbfffffffbfffffffbfffffffffffffffbfffffffbfffffffffffffffffffffffdfffffffaffffc8f9ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
m_LayerCollisionMatrix: ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
m_AutoSimulation: 1
m_AutoSyncTransforms: 0
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m_ClothInterCollisionSettingsToggle: 0
m_ClothGravity: {x: 0, y: -9.81, z: 0}
m_ContactPairsMode: 0
m_BroadphaseType: 0
m_WorldBounds:
@ -32,5 +31,4 @@ PhysicsManager:
m_FrictionType: 0
m_EnableEnhancedDeterminism: 0
m_EnableUnifiedHeightmaps: 1
m_SolverType: 0
m_DefaultMaxAngularSpeed: 7
m_DefaultMaxAngluarSpeed: 7

View File

@ -38,7 +38,7 @@ GraphicsSettings:
m_PreloadedShaders: []
m_SpritesDefaultMaterial: {fileID: 10754, guid: 0000000000000000f000000000000000,
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View File

@ -1,223 +0,0 @@
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@ -4,7 +4,7 @@
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companyName: DefaultCompany
productName: Tutorials-Movement-SlidingASphere
productName: Tutorials-Basics-MathematicalSurfaces
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View File

@ -1,2 +1,2 @@
m_EditorVersion: 2019.4.19f1c1
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m_EditorVersion: 2019.4.18f1c1
m_EditorVersionWithRevision: 2019.4.18f1c1 (6ddd89a99571)

View File

@ -13,9 +13,9 @@ TagManager:
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