Author: kpark

Perspective & Orthogonal Projection Matrix

Projection = glm::perspective(g_fovy, g_aspect, g_zNear, g_zFar);

Projection = glm::ortho(-5.0f, 5.0f, -5.0f, 5.0f, g_zNear, g_zFar);

Camera & View Matrix

camera class를 사용하여 x/y/x축 카메라의 위치이동과 x/y/x축 카메라의 방향이동
F1&F2 – x축 카메라 위치이동
F3&F4 – y축 카메라 위치이동
F5&F6 – z축 카메라 위치이동
F7&F8 – x축 카메라 방향이동 (PITCH)
F9&F10 – y축 카메라 방향이동 (YAW)
HOME&END – z축 카메라 방향이동 (ROLL)

template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAt(tvec3<T, P> const & eye, tvec3<T, P> const & center, tvec3<T, P> const & up)
{
# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED
return lookAtLH(eye, center, up);
# else
return lookAtRH(eye, center, up);
# endif
}

template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAtRH
(
tvec3<T, P> const & eye,
tvec3<T, P> const & center,
tvec3<T, P> const & up
)
{
tvec3<T, P> const f(normalize(center – eye));
tvec3<T, P> const s(normalize(cross(f, up)));
tvec3<T, P> const u(cross(s, f));

tmat4x4<T, P> Result(1);
Result[0][0] = s.x;
Result[1][0] = s.y;
Result[2][0] = s.z;
Result[0][1] = u.x;
Result[1][1] = u.y;
Result[2][1] = u.z;
Result[0][2] =-f.x;
Result[1][2] =-f.y;
Result[2][2] =-f.z;
Result[3][0] =-dot(s, eye);
Result[3][1] =-dot(u, eye);
Result[3][2] = dot(f, eye);
return Result;
}

template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAtLH
(
tvec3<T, P> const & eye,
tvec3<T, P> const & center,
tvec3<T, P> const & up
)
{
tvec3<T, P> const f(normalize(center – eye));
tvec3<T, P> const s(normalize(cross(up, f)));
tvec3<T, P> const u(cross(f, s));

tmat4x4<T, P> Result(1);
Result[0][0] = s.x;
Result[1][0] = s.y;
Result[2][0] = s.z;
Result[0][1] = u.x;
Result[1][1] = u.y;
Result[2][1] = u.z;
Result[0][2] = f.x;
Result[1][2] = f.y;
Result[2][2] = f.z;
Result[3][0] = -dot(s, eye);
Result[3][1] = -dot(u, eye);
Result[3][2] = -dot(f, eye);
return Result;
}

Orthographic Projection

template <typename T>
 GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
 (
  T left,
  T right,
  T bottom,
  T top,
  T zNear,
  T zFar
 )
 {
  tmat4x4<T, defaultp> Result(1);
  Result[0][0] = static_cast<T>(2) / (right - left);
  Result[1][1] = static_cast<T>(2) / (top - bottom);
  Result[2][2] = - static_cast<T>(2) / (zFar - zNear);
  Result[3][0] = - (right + left) / (right - left);
  Result[3][1] = - (top + bottom) / (top - bottom);
  Result[3][2] = - (zFar + zNear) / (zFar - zNear);
  return Result;
 }

Perspective Projection

 template <typename T>
 GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustum
 (
  T left,
  T right,
  T bottom,
  T top,
  T nearVal,
  T farVal
 )
 {
  tmat4x4<T, defaultp> Result(0);
  Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
  Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
  Result[2][0] = (right + left) / (right - left);
  Result[2][1] = (top + bottom) / (top - bottom);
  Result[2][2] = -(farVal + nearVal) / (farVal - nearVal);
  Result[2][3] = static_cast<T>(-1);
  Result[3][2] = -(static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
  return Result;
 }

http://www.songho.ca/opengl/gl_projectionmatrix.html

lab9-GeometryPositionColorOrientation-src

// Yaw/Pitch/Roll -> Rotation Matrix

glm::yawPitchRoll(yaw, pitch, roll) ;

float yaw, // by y-axis (in radians)

float pitch, // by x-axis (in radians)

float roll // by z-axis (in radians)

// R1 != R2

glm::mat4 R1, R2, Rx, Ry, Rz;

Ry = glm::rotate(glm::mat4(1), 60, glm::vec3(0, 1, 0));

Rx = glm::rotate(glm::mat4(1), 30, glm::vec3(1, 0, 0));

Rz = glm::rotate(glm::mat4(1), 45, glm::vec3(0, 0, 1));

R1 = Ry * Rx * Rz; // world coordinate system에서 rotation

R2 = glm::yawPitchRoll(60, 30, 45); // Creates a 3D 4 * 4 homogeneous rotation matrix from euler angles (YXZ). local coordinate system에서 rotation

https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline

// Loop around the total time if necessary
if (elapsedTime >= endTime) {
    if (loop) {
        while (elapsedTime > endTime)
            elapsedTime -= endTime;
    }
    else {
        position = frames[frames.size() - 1].position;
        return;
    }
}

int i = 0;
// Find the index of the current frame
while (frames[i+1].time < elapsedTime) i++;
	
// Find the time since the beginning of this frame
elapsedTime -= frames[i].time;

// Find how far we are between the current and next frame (0 to 1)
float fraction = (float)(elapsedTime / (frames[i + 1].time - frames[i].time));

// Interpolate position and rotation values between frames
position = glm::catmullRom (
                   frames[wrap(i - 1, frames.size() - 1)].position,
                   frames[wrap(i, frames.size() - 1)].position,
                   frames[wrap(i + 1, frames.size() - 1)].position,
                   frames[wrap(i + 2, frames.size() - 1)].position,
                   fraction);

template<typename genType> 
GLM_FUNC_QUALIFIER genType catmullRom(
		genType const& v1,
		genType const& v2,
		genType const& v3,
		genType const& v4,
		typename genType::value_type const& s
	) {
    typename genType::value_type s2 = pow2(s);
    typename genType::value_type s3 = pow3(s);

    typename genType::value_type f1 = -s3 + typename genType::value_type(2) * s2 - s;
    typename genType::value_type f2 = typename genType::value_type(3) * s3 - typename genType::value_type(5) * s2 + typename genType::value_type(2);
    typename genType::value_type f3 = typename genType::value_type(-3) * s3 + typename genType::value_type(4) * s2 + s;
    typename genType::value_type f4 = s3 - s2;

    return (f1 * v1 + f2 * v2 + f3 * v3 + f4 * v4) / typename genType::value_type(2);
}

http://www.lighthouse3d.com/tutorials/maths/catmull-rom-spline/

f(x) = [1, x, x^2, x^3] * M * [v1, v2, v3, v4]

/* Coefficients for Matrix M */
#define M11	 0.0
#define M12	 1.0
#define M13	 0.0
#define M14	 0.0
#define M21	-0.5
#define M22	 0.0
#define M23	 0.5
#define M24	 0.0
#define M31	 1.0
#define M32	-2.5
#define M33	 2.0
#define M34	-0.5
#define M41	-0.5
#define M42	 1.5
#define M43	-1.5
#define M44	 0.5

double catmullRomSpline(float x, float v1,float v2, float v3,float v4) {
	double c1,c2,c3,c4;

	c1 =  	      M12*v2;
	c2 = M21*v1          + M23*v3;
	c3 = M31*v1 + M32*v2 + M33*v3 + M34*v4;
	c4 = M41*v1 + M42*v2 + M43*v3 + M44*v4;

	return(((c4*x + c3)*x +c2)*x + c1);
}

lab8
SimpleSa
lab8-GeometryPositionColorHierachicalTransformation-src

-Simple Car (c-key)

-Solar System (s-key)

-Robot (r-key)

-Mobile (m-key)

-Geo (g-key)