proper lookat and perspective matrix

This commit is contained in:
Trammell hudson 2018-02-27 08:21:49 -05:00
parent 7391a667fe
commit 060a4d472d
Failed to extract signature
3 changed files with 109 additions and 51 deletions

146
camera.c
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@ -11,26 +11,24 @@
struct _camera_t struct _camera_t
{ {
float zoom; float near;
v3_t eye; float far;
float r[3][3]; float r[4][4];
}; };
camera_t * camera_t *
camera_new( camera_new(
v3_t eye, v3_t eye,
float phi, v3_t lookat,
float theta, v3_t up
float psi
) )
{ {
camera_t * c = calloc(1, sizeof(*c)); camera_t * c = calloc(1, sizeof(*c));
if (!c) if (!c)
return NULL; return NULL;
c->zoom = 4096; camera_setup(c, eye, lookat, up);
camera_setup(c, eye, phi, theta, psi);
return c; return c;
} }
@ -39,64 +37,126 @@ void
camera_setup( camera_setup(
camera_t * const c, camera_t * const c,
v3_t eye, v3_t eye,
float phi, v3_t lookat,
float theta, v3_t up
float psi
) )
{ {
const float sx = sin(phi); // compute the basis for the camera
const float cx = cos(phi); // negative look direction from eye to destination
const float sy = sin(theta); v3_t w = v3_norm(v3_sub(eye, lookat));
const float cy = cos(theta);
const float sz = sin(psi);
const float cz = cos(psi);
c->r[0][0] = cy * cz; // compute the side axis
c->r[0][1] = (-cy * sz) + (sx * sy * cz); v3_t u = v3_norm(v3_cross(up, w));
c->r[0][2] = ( sx * sz) + (cx * sy * cz);
c->r[1][0] = cx * sz; // and the "up" normal
c->r[1][1] = ( cx * cz) + (sx * sy * sz); v3_t v = v3_norm(v3_cross(w, u));
c->r[1][2] = (-sx * cz) + (cx * sy * sz);
c->r[2][0] = -sy; float cam[4][4] = {};
c->r[2][1] = sx * cy;
c->r[2][2] = cx * cy;
c->eye = eye; cam[0][0] = u.p[0];
} cam[1][0] = u.p[1];
cam[2][0] = u.p[2];
cam[3][0] = 0;
cam[0][1] = v.p[0];
cam[1][1] = v.p[1];
cam[2][1] = v.p[2];
cam[3][1] = 0;
cam[0][2] = w.p[0];
cam[1][2] = w.p[1];
cam[2][2] = w.p[2];
cam[3][2] = 0;
// compute u dot c, v dot c, w, dot c
cam[0][3] = -v3_dot(lookat, u);
cam[1][3] = -v3_dot(lookat, v);
cam[2][3] = -v3_dot(lookat, w);
cam[3][3] = 1;
for(int i = 0 ; i < 4 ; i++)
{
for(int j = 0 ; j < 4 ; j++)
fprintf(stderr, " %+5.3f", cam[i][j]);
fprintf(stderr, "\n");
}
// now compute the perspective projection matrix
float fov = 60;
float s = 1.0 / tan(fov * M_PI / 180 / 2);
c->near = 1.0;
c->far = 200;
float f1 = - c->far * (c->far - c->near);
float f2 = - c->far * c->near / (c->far - c->near);
float pers[4][4] = {
{ s, 0, 0, 0 },
{ 0, s, 0, 0 },
{ 0, 0, f1, -1 },
{ 0, 0, f2, 0 },
};
// and apply it to the camera matrix to generate transform
for(int i = 0 ; i < 4 ; i++)
{
for(int j = 0 ; j < 4 ; j++)
{
float d = 0;
for(int k = 0 ; k < 4 ; k++)
d += cam[i][k] * pers[k][j];
c->r[i][j] = d;
}
}
for(int i = 0 ; i < 4 ; i++)
{
for(int j = 0 ; j < 4 ; j++)
fprintf(stderr, " %+5.3f", c->r[i][j]);
fprintf(stderr, "\n");
}
}
/** Transform a XYZ point into a screen point. /** Transform a XYZ point into a screen point.
* *
* Returns 0 if this is behind us. Perhaps it should do a z buffer? * Returns 0 if this is behind us. Perhaps it should do a z buffer?
* https://en.wikipedia.org/wiki/3D_projection
*/ */
int int
camera_project( camera_project(
const camera_t * const c, const camera_t * const c,
const v3_t * const v, const v3_t * const v_in,
v3_t * const v_out v3_t * const v_out
) )
{ {
v3_t p = c->eye; float v[4] = { v_in->p[0], v_in->p[1], v_in->p[2], 1 };
float p[4] = { 0, 0, 0, 0};
for (int i = 0 ; i < 4 ; i++)
for (int j = 0 ; j < 4 ; j++)
p[i] += c->r[j][i] * v[j];
if(0) fprintf(stderr, "%.2f,%.2f,%.2f -> %.2f,%.2f,%.2f,%.2f\n",
v[0], v[1], v[2],
p[0], p[1], p[2], p[3]
);
/*
for (int i = 0 ; i < 3 ; i++) for (int i = 0 ; i < 3 ; i++)
for (int j = 0 ; j < 3 ; j++) p[i] /= p[3];
p.p[i] += c->r[i][j] * v->p[j]; */
p[2] /= p[3];
// what if p->p[2] == 0?
// Transform to screen coordinate frame, // Transform to screen coordinate frame,
// is this rotating? // and return it to the caller
float px = p.p[1] / p.p[2]; v_out->p[0] = p[0] * 100;
float py = p.p[0] / p.p[2]; v_out->p[1] = p[1] * 100;
float pz = p.p[2] / c->zoom; v_out->p[2] = p[2] * 100;
// return it to the caller
v_out->p[0] = px * c->zoom;
v_out->p[1] = py * c->zoom;
v_out->p[2] = pz * c->zoom;
// what if p->p[4] == 0?
// pz < 0 == The point is behind us; do not display? // pz < 0 == The point is behind us; do not display?
return pz <= 0 ? 0 : 1; if (p[2] < c->near || p[2] > c->far)
return 0;
return 1;
} }

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@ -7,18 +7,16 @@ typedef struct _camera_t camera_t;
extern camera_t * extern camera_t *
camera_new( camera_new(
v3_t eye, v3_t eye,
float phi, v3_t lookat,
float theta, v3_t up
float psi
); );
extern void extern void
camera_setup( camera_setup(
camera_t * const c, camera_t * const c,
v3_t eye, v3_t eye,
float phi, v3_t lookat,
float theta, v3_t up
float psi
); );
/** Transform a XYZ point into a screen point. /** Transform a XYZ point into a screen point.

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@ -669,9 +669,9 @@ int main(
// looking at (0,0,0) // looking at (0,0,0)
v3_t eye = { { 100, 20, 50 } }; v3_t eye = { { -100, 40, 50 } };
v3_t lookat = { { 0, 0, 0 } }; v3_t lookat = { { 0, 0, 0 } };
v3_t up = { { 0, 0, 1 } }; v3_t up = { { 0, -1, 0 } };
const camera_t * const cam = camera_new(eye, lookat, up); const camera_t * const cam = camera_new(eye, lookat, up);
printf("<svg xmlns=\"http://www.w3.org/2000/svg\">\n"); printf("<svg xmlns=\"http://www.w3.org/2000/svg\">\n");