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3D 360 degrees rotation around x axis

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How do we rotate the camera around x axis 360 degrees, without having the strange effect as in my video below? 

Mine behaves exactly the same way spherical coordinates would, I'm using euler angles.

Tried googling, but couldn't find a proper answer, guessing I don't know what exactly to google for, googled 'rotate 360 around x axis', got no proper answers.

 

References:

Code: https://pastebin.com/Hcshj3FQ

The video shows the difference between blender and my rotation:

 

Edited by dud3

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I would suggest using a parametrization of rotations that doesn't have a region where things get wacky. Either orthogonal matrices or quaternions would do.

 

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I think I'm stuck, I'm just trying to achieve the same rotation around the x axis as in blender.

The video shows the difference between blender and my rotation:

 

Edited by dud3

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You should have a notion of what the current attitude of your object is (i.e., the rotation that brings it from its initial position to its current position). When the mouse is clicked you create a new rotation, which depends only on the point where the mouse was initially clicked and its current position (perhaps just depends on the vector between those). While the mouse button is down, you display the object as having attitude (current_attitude * mouse_rotation). When the mouse button is released, you bake the mouse rotation into the attitude (`current_attitude *= mouse_rotation').

In the paragraph above I have used multiplicative notation to represent composition of rotations. Composition of rotations is hard if you are using Euler angles. But if you are using matrices or quaternions, it literally is a multiplication (be careful to get the order right, because it matters).

 

Edited by alvaro

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This is the current code, under dragTPSInput(...):
 

#pragma once

#include <glm.hpp>
#include <gtc/matrix_transform.hpp>
#include <gtc/type_ptr.hpp>

#include "InputHandler.h"
#include "Vector2D.h"

class Camera 
{
public:

	glm::vec3 m_position;
	
	glm::vec3 m_front;
	glm::vec3 m_up;
	glm::vec3 m_right;

	glm::vec3 m_worldup;

	float m_yaw;
	float m_pitch;

	float m_zoom;

	bool m_enableInput;

	// Mouse
	float m_mouseSensitivity;

	enum class direction { in, out, right, left };

	Camera(glm::vec3 position = glm::vec3(0.0f, 0.0f, 0.0f), 
		glm::vec3 up = glm::vec3(0.0f, 1.0f, 0.0f), 
		float yaw = -90.0f,
		float pitch = 0.0,
		float zoom = 1.0f,
		float mouseSensitivity = 0.05f) :
		m_front(glm::vec3(0.0f, 0.0f, -1.0f)), 
		m_enableInput(false)
	{
		m_position = position;

		m_yaw = yaw;
		m_pitch = pitch;

		m_worldup = up;

		m_zoom = zoom;
		m_mouseSensitivity = mouseSensitivity;

		updateCameraVectors();
	}

	void lookAt()
	{
	}

	void move(direction d)
	{
		if (d == direction::in)
			m_position -= m_front;
		
		if (d == direction::out)
			m_position += m_front;

		if(d == direction::right)
			m_position += glm::normalize(glm::cross(m_front, m_up)) * m_mouseSensitivity;

		if(d == direction::left)
			m_position -= glm::normalize(glm::cross(m_front, m_up)) * m_mouseSensitivity;
	}
	
	void rotate()
	{
	}

	void zoom()
	{
	}

	void scrollInput()
	{
	}

	void keyboardInput()
	{
		// todo: give the user ability to adjust input keys

		if (_inHandler->onKeyDown(SDL_SCANCODE_W)) {
			move(direction::in);
		}
		if (_inHandler->onKeyDown(SDL_SCANCODE_S)) {
			move(direction::out);
		}
		if (_inHandler->onKeyDown(SDL_SCANCODE_D)) {
			move(direction::right);
		}
		if (_inHandler->onKeyDown(SDL_SCANCODE_A)) {
			move(direction::left);
		}
	}

	void dragFPSInput(Vector2D* mouseMoveDiff, bool constrainPitch = true)
	{
		m_yaw += mouseMoveDiff->getX(); // offsetx
		m_pitch += -(mouseMoveDiff->getY()); // offsety

		// Make sure that when pitch is out of bounds, screen doesn't get flipped
		if (constrainPitch)
		{
			if (m_pitch > 89.0f)
				m_pitch = 89.0f;
			if (m_pitch < -89.0f)
				m_pitch = -89.0f;
		}

		// Update Front, Right and Up Vectors using the updated Eular angles
		updateCameraVectors();
	}

	void dragTPSInput(Vector2D* mouseMoveDiff)
	{
		// m_position = glm::rotate(m_position, -mouseMoveDiff->getY() * m_mouseSensitivity, glm::vec3(1, 0, 0));
		// m_position = glm::rotate(m_position, -mouseMoveDiff->getX() * m_mouseSensitivity, glm::vec3(0, 1, 0));

		glm::quat rot = glm::angleAxis(glm::radians(-mouseMoveDiff->getY()), glm::vec3(1, 0, 0));
		rot = rot * glm::angleAxis(glm::radians(-mouseMoveDiff->getX()), glm::vec3(0, 1, 0));

		glm::mat4 rotMatrix = glm::mat4_cast(rot);

		glm::vec4 pos = glm::vec4(m_position.x, m_position.y, m_position.z, 1.0f);

		pos = rotMatrix * pos;

		m_position.x = pos.x;
		m_position.y = pos.y;
		m_position.z = pos.z;

		updateCameraVectors();
	}

	void onInput(bool drag = true, bool scroll = true, bool keyboard = false)
	{
		if (drag)
			if (_inHandler->getMouseButtonState(_inHandler->mouse_buttons::LEFT))
				if(_inHandler->isMouseMovig())
					dragTPSInput(_inHandler->getMouseMoveDiff());

		if (scroll)
			scrollInput();

		if (keyboard)
			keyboardInput();
	}

	// Returns the view matrix calculated using Eular Angles and the LookAt Matrix
	glm::mat4 getViewMatrix()
	{
		glm::vec3 pos = glm::vec3(m_position.x, m_position.y, m_position.z);
		return glm::lookAt(pos, m_front, m_up);
	}

private:
	void updateCameraVectors()
	{
		// Calculate the new Front vector
		glm::vec3 front;
		front.x = cos(glm::radians(m_yaw)) * cos(glm::radians(m_pitch));
		front.y = sin(glm::radians(m_pitch));
		front.z = sin(glm::radians(m_yaw)) * cos(glm::radians(m_pitch));

		m_front = glm::normalize(front);

		// Also re-calculate the Right and Up vector
		// Normalize the vectors, because their length gets closer to 0 the more you look up or down which results in slower movement.
		m_right = glm::normalize(glm::cross(m_front, m_worldup)); 
		
		m_up = glm::normalize(glm::cross(m_right, m_front));
	}

	InputHandler* _inHandler = TheInputHandler::Instance();
};

 

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      Setting the Pipeline State and Committing Shader Resources
      Before any draw or compute command can be invoked, the pipeline state needs to be bound to the context:
      m_pContext->SetPipelineState(m_pPSO); Under the hood, the engine sets the internal PSO object in the command list or calls all the required native API functions to properly configure all pipeline stages.
      The next step is to bind all required shader resources to the GPU pipeline, which is accomplished by IDeviceContext::CommitShaderResources() method:
      m_pContext->CommitShaderResources(m_pSRB, COMMIT_SHADER_RESOURCES_FLAG_TRANSITION_RESOURCES); The method takes a pointer to the shader resource binding object and makes all resources the object holds available for the shaders. In the case of D3D12, this only requires setting appropriate descriptor tables in the command list. For older APIs, this typically requires setting all resources individually.
      Next-generation APIs require the application to track the state of every resource and explicitly inform the system about all state transitions. For instance, if a texture was used as render target before, while the next draw command is going to use it as shader resource, a transition barrier needs to be executed. Diligent Engine does the heavy lifting of state tracking.  When CommitShaderResources() method is called with COMMIT_SHADER_RESOURCES_FLAG_TRANSITION_RESOURCES flag, the engine commits and transitions resources to correct states at the same time. Note that transitioning resources does introduce some overhead. The engine tracks state of every resource and it will not issue the barrier if the state is already correct. But checking resource state is an overhead that can sometimes be avoided. The engine provides IDeviceContext::TransitionShaderResources() method that only transitions resources:
      m_pContext->TransitionShaderResources(m_pPSO, m_pSRB); In some scenarios it is more efficient to transition resources once and then only commit them.
      Invoking Draw Command
      The final step is to set states that are not part of the PSO, such as render targets, vertex and index buffers. Diligent Engine uses Direct3D11-syle API that is translated to other native API calls under the hood:
      ITextureView *pRTVs[] = {m_pRTV}; m_pContext->SetRenderTargets(_countof( pRTVs ), pRTVs, m_pDSV); // Clear render target and depth buffer const float zero[4] = {0, 0, 0, 0}; m_pContext->ClearRenderTarget(nullptr, zero); m_pContext->ClearDepthStencil(nullptr, CLEAR_DEPTH_FLAG, 1.f); // Set vertex and index buffers IBuffer *buffer[] = {m_pVertexBuffer}; Uint32 offsets[] = {0}; Uint32 strides[] = {sizeof(MyVertex)}; m_pContext->SetVertexBuffers(0, 1, buffer, strides, offsets, SET_VERTEX_BUFFERS_FLAG_RESET); m_pContext->SetIndexBuffer(m_pIndexBuffer, 0); Different native APIs use various set of function to execute draw commands depending on command details (if the command is indexed, instanced or both, what offsets in the source buffers are used etc.). For instance, there are 5 draw commands in Direct3D11 and more than 9 commands in OpenGL with something like glDrawElementsInstancedBaseVertexBaseInstance not uncommon. Diligent Engine hides all details with single IDeviceContext::Draw() method that takes takes DrawAttribs structure as an argument. The structure members define all attributes required to perform the command (primitive topology, number of vertices or indices, if draw call is indexed or not, if draw call is instanced or not, if draw call is indirect or not, etc.). For example:
      DrawAttribs attrs; attrs.IsIndexed = true; attrs.IndexType = VT_UINT16; attrs.NumIndices = 36; attrs.Topology = PRIMITIVE_TOPOLOGY_TRIANGLE_LIST; pContext->Draw(attrs); For compute commands, there is IDeviceContext::DispatchCompute() method that takes DispatchComputeAttribs structure that defines compute grid dimension.
      Source Code
      Full engine source code is available on GitHub and is free to use. The repository contains two samples, asteroids performance benchmark and example Unity project that uses Diligent Engine in native plugin.
      AntTweakBar sample is Diligent Engine’s “Hello World” example.

       
      Atmospheric scattering sample is a more advanced example. It demonstrates how Diligent Engine can be used to implement various rendering tasks: loading textures from files, using complex shaders, rendering to multiple render targets, using compute shaders and unordered access views, etc.

      Asteroids performance benchmark is based on this demo developed by Intel. It renders 50,000 unique textured asteroids and allows comparing performance of Direct3D11 and Direct3D12 implementations. Every asteroid is a combination of one of 1000 unique meshes and one of 10 unique textures.

      Finally, there is an example project that shows how Diligent Engine can be integrated with Unity.

      Future Work
      The engine is under active development. It currently supports Windows desktop, Universal Windows and Android platforms. Direct3D11, Direct3D12, OpenGL/GLES backends are now feature complete. Vulkan backend is coming next, and support for more platforms is planned.
    • By kevinyu
      Original Post: Limitless Curiosity
      Out of various phases of the physics engine. Constraint Resolution was the hardest for me to understand personally. I need to read a lot of different papers and articles to fully understand how constraint resolution works. So I decided to write this article to help me understand it more easily in the future if, for example, I forget how this works.
      This article will tackle this problem by giving an example then make a general formula out of it. So let us delve into a pretty common scenario when two of our rigid bodies collide and penetrate each other as depicted below.

      From the scenario above we can formulate:
      \(\(d = ((\vec{p1} + \vec{r1}) - (\vec{p2} + \vec{r2}) \cdot \vec{n}\\)
      We don't want our rigid bodies to intersect each other, thus we construct a constraint where the penetration depth must be more than zero.
      \(C: d>=0\)
      This is an inequality constraint, we can transform it to a more simple equality constraint by only solving it if two bodies are penetrating each other. If two rigid bodies don't collide with each other, we don't need any constraint resolution. So:
      if d>=0, do nothing else if d < 0 solve C: d = 0
      Now we solve this constraint by calculating $\Delta \vec{p1},\Delta \vec{p2},\Delta \vec{r1},and \Delta \vec{r2}$ that cause the constraint above satisfied. This method is called the position-based method. This will satisfy the above constraint immediately in the current frame and might cause a jittery effect.
      A much more modern and preferable method that is used in Box2d, Chipmunk, Bullet and my physics engine is called the impulse-based method. In this method, we derive a velocity constraint equation from the position constraint equation above.

      We are working in 2D so angular velocity and the cross result of two vectors are scalars.
      Next, we need to find $\Delta V$ or impulse to satisfy the velocity constraint. This $\Delta V$ is caused by a force. We call this force 'constraint force'. Constraint force only exerts a force on the direction of illegal movement in our case the penetration normal. We don't want this force to do any work, contribute or restrict any motion of legal direction.

      $\lambda$ is a scalar, called Lagrangian multiplier. To understand why constraint force working on \(J^T\) $J^{T}$ direction (remember J is a 12 by 1 matrix, so $J^{T}$ is a 1 by 12 matrix or a 12-dimensional vector), try to remember the equation for a three-dimensional plane.

      Now we can draw similarity between equation(1) and equation(2), where $\vec{n}^{T}$ is similar to J and $\vec{v}$ is similar to V. So we can interpret equation(1) as a 12 dimensional plane, we can conclude that $J^{T}$ as the normal of this plane. If a point is outside a plane, the shortest distance from this point to the surface is the normal direction.

      After we calculate the Lagrangian multiplier, we have a way to get back the impulse from equation(3). Then, we can apply this impulse to each rigid body.
      Baumgarte Stabilization
      Note that solving the velocity constraint doesn't mean that we satisfy the position constraint. When we solve the velocity constraint, there is already a violation in the position constraint. We call this violation position drift. What we achieve is stopping the two bodies from penetrating deeper (The penetration depth will stop growing). It might be fine for a slow-moving object as the position drift is not noticeable, but it will be a problem as the object moving faster. The animation below demonstrates what happens when we solve the velocity constraint.
      [caption id="attachment_38" align="alignnone" width="800"]
      So instead of purely solving the velocity constraint, we add a bias term to fix any violation that happens in position constraint. 

      So what is the value of the bias? As mentioned before we need this bias to fix positional drift. So we want this bias to be in proportion to penetration depth.

      This method is called Baumgarte Stabilization and $\beta$ is a baumgarte term. The right value for this term might differ for different scenarios. We need to tweak this value between 0 and 1 to find the right value that makes our simulation stable.

       
      Sequential Impulse
      If our world consists only of two rigid bodies and one contact constraint. Then the above method will work decently. But in most games, there are more than two rigid bodies. One body can collide and penetrate with two or more bodies. We need to satisfy all the contact constraint simultaneously. For a real-time application, solving all these constraints simultaneously is not feasible. Erin Catto proposes a practical solution, called sequential impulse. The idea here is similar to Project Gauss-Seidel. We calculate $\lambda$ and $\Delta V$ for each constraint one by one, from constraint one to constraint n(n = number of constraint). After we finish iterating through the constraints and calculate $\Delta V$, we repeat the process from constraint one to constraint n until the specified number of iteration. This algorithm will converge to the actual solution.The more we repeat the process, the more accurate the result will be. In Box2d, Erin Catto set ten as the default for the number of iteration.
      Another thing to notice is that while we satisfy one constraint we might unintentionally satisfy another constraint. Say for example that we have two different contact constraint on the same rigid body.

      When we solve $\dot{C1}$, we might incidentally make $\dot{d2} >= 0$. Remember that equation(5), is a formula for $\dot{C}: \dot{d} = 0$ not $\dot{C}: \dot{d} >= 0$. So we don't need to apply it to $\dot{C2}$ anymore. We can detect this by looking at the sign of $\lambda$. If the sign of $\lambda$ is negative, that means the constraint is already satisfied. If we use this negative lambda as an impulse, it means we pull it closer instead of pushing it apart. It is fine for individual $\lambda$ to be negative. But, we need to make sure the accumulation of $\lambda$ is not negative. In each iteration, we add the current lambda to normalImpulseSum. Then we clamp the normalImpulseSum between 0 and positive infinity. The actual Lagrangian multiplier that we will use to calculate the impulse is the difference between the new normalImpulseSum and the previous normalImpulseSum
      Restitution
      Okay, now we have successfully resolve contact penetration in our physics engine. But what about simulating objects that bounce when a collision happens. The property to bounce when a collision happens is called restitution. The coefficient of restitution, denoted $C_{r}$, is the ratio of the parting speed after the collision and the closing speed before the collision.

      The coefficient of restitution only affects the velocity along the normal direction. So we need to do the dot operation with the normal vector.

      Notice that in this specific case the $V_{initial}$ is similar to JV. If we look back at our constraint above, we set $\dot{d}$ to zero because we assume that the object does not bounce back($C_{r}=0$).So, if $C_{r} != 0$, instead of 0, we can modify our constraint so the desired velocity is $V_{final}$.

      We can merge our old bias term with the restitution term to get a new bias value.

      // init constraint // Calculate J(M^-1)(J^T). This term is constant so we can calculate this first for (int i = 0; i < constraint->numContactPoint; i++) { ftContactPointConstraint *pointConstraint = &constraint->pointConstraint; pointConstraint->r1 = manifold->contactPoints.r1 - (bodyA->transform.center + bodyA->centerOfMass); pointConstraint->r2 = manifold->contactPoints.r2 - (bodyB->transform.center + bodyB->centerOfMass); real kNormal = bodyA->inverseMass + bodyB->inverseMass; // Calculate r X normal real rnA = pointConstraint->r1.cross(constraint->normal); real rnB = pointConstraint->r2.cross(constraint->normal); // Calculate J(M^-1)(J^T). kNormal += (bodyA->inverseMoment * rnA * rnA + bodyB->inverseMoment * rnB * rnB); // Save inverse of J(M^-1)(J^T). pointConstraint->normalMass = 1 / kNormal; pointConstraint->positionBias = m_option.baumgarteCoef * manifold->penetrationDepth; ftVector2 vA = bodyA->velocity; ftVector2 vB = bodyB->velocity; real wA = bodyA->angularVelocity; real wB = bodyB->angularVelocity; ftVector2 dv = (vB + pointConstraint->r2.invCross(wB) - vA - pointConstraint->r1.invCross(wA)); //Calculate JV real jnV = dv.dot(constraint->normal pointConstraint->restitutionBias = -restitution * (jnV + m_option.restitutionSlop); } // solve constraint while (numIteration > 0) { for (int i = 0; i < m_constraintGroup.nConstraint; ++i) { ftContactConstraint *constraint = &(m_constraintGroup.constraints); int32 bodyIDA = constraint->bodyIDA; int32 bodyIDB = constraint->bodyIDB; ftVector2 normal = constraint->normal; ftVector2 tangent = normal.tangent(); for (int j = 0; j < constraint->numContactPoint; ++j) { ftContactPointConstraint *pointConstraint = &(constraint->pointConstraint[j]); ftVector2 vA = m_constraintGroup.velocities[bodyIDA]; ftVector2 vB = m_constraintGroup.velocities[bodyIDB]; real wA = m_constraintGroup.angularVelocities[bodyIDA]; real wB = m_constraintGroup.angularVelocities[bodyIDB]; //Calculate JV. (jnV = JV, dv = derivative of d, JV = derivative(d) dot normal)) ftVector2 dv = (vB + pointConstraint->r2.invCross(wB) - vA - pointConstraint->r1.invCross(wA)); real jnV = dv.dot(normal); //Calculate Lambda ( lambda real nLambda = (-jnV + pointConstraint->positionBias / dt + pointConstraint->restitutionBias) * pointConstraint->normalMass; // Add lambda to normalImpulse and clamp real oldAccumI = pointConstraint->nIAcc; pointConstraint->nIAcc += nLambda; if (pointConstraint->nIAcc < 0) { pointConstraint->nIAcc = 0; } // Find real lambda real I = pointConstraint->nIAcc - oldAccumI; // Calculate linear impulse ftVector2 nLinearI = normal * I; // Calculate angular impulse real rnA = pointConstraint->r1.cross(normal); real rnB = pointConstraint->r2.cross(normal); real nAngularIA = rnA * I; real nAngularIB = rnB * I; // Apply linear impulse m_constraintGroup.velocities[bodyIDA] -= constraint->invMassA * nLinearI; m_constraintGroup.velocities[bodyIDB] += constraint->invMassB * nLinearI; // Apply angular impulse m_constraintGroup.angularVelocities[bodyIDA] -= constraint->invMomentA * nAngularIA; m_constraintGroup.angularVelocities[bodyIDB] += constraint->invMomentB * nAngularIB; } } --numIteration; }  
      General Step to Solve Constraint
      In this article, we have learned how to solve contact penetration by defining it as a constraint and solve it. But this framework is not only used to solve contact penetration. We can do many more cool things with constraints like for example implementing hinge joint, pulley, spring, etc.
      So this is the step-by-step of constraint resolution:
      Define the constraint in the form $\dot{C}: JV + b = 0$. V is always $\begin{bmatrix} \vec{v1} \\ w1 \\ \vec{v2} \\ w2\end{bmatrix}$ for every constraint. So we need to find J or the Jacobian Matrix for that specific constraint. Decide the number of iteration for the sequential impulse. Next find the Lagrangian multiplier by inserting velocity, mass, and the Jacobian Matrix into this equation: Do step 3 for each constraint, and repeat the process as much as the number of iteration. Clamp the Lagrangian multiplier if needed. This marks the end of this article. Feel free to ask if something is still unclear. And please inform me if there are inaccuracies in my article. Thank you for reading.
      NB: Box2d use sequential impulse, but does not use baumgarte stabilization anymore. It uses full NGS to resolve the position drift. Chipmunk still use baumgarte stabilization.
      References
      Allen Chou's post on Constraint Resolution A Unified Framework for Rigid Body Dynamics An Introduction to Physically Based Modeling: Constrained Dynamics Erin Catto's Box2d and presentation on constraint resolution Falton Debug Visualizer 18_01_2018 22_40_12.mp4
      equation.svg

    • By regnar
      Hi!
      I've been trying to implement simple virtual globe rendering system using "3D Engine Design for Virtual Globes" book as a reference.  What I do is I use 6 planes to form a cube, send it to GPU and use vertex shader to form a sphere and add random noise to simulate surface of the planet. The problem is how do I do CPU work on the vertex data from now on - how do I get world space coordinates of a terrain patch to perform LOD techniques, how do I do camera-terrain collision detection etc. ?
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