void csm_calc_minsphere(struct sphere* bounds, const struct frustum* f,
const struct mat3f* view, const struct mat3f* view_inv)
{
/* reference:
* http://www.gamedev.net/topic/604797-minimum-bounding-sphere-of-a-frustum/
*/
struct vec3f a;
struct vec3f b;
struct vec3f p;
struct vec3f tmp;
vec3_transformsrt(&a, &f->points[1], view);
vec3_transformsrt(&b, &f->points[5], view);
float z = (vec3_dot(&b, &b) - vec3_dot(&a, &a))/(2.0f*(b.z - a.z));
vec3_setf(&p, 0.0f, 0.0f, z);
vec3_transformsrt(&p, &p, view_inv);
sphere_setf(bounds, p.x, p.y, p.z, vec3_len(vec3_sub(&tmp, &f->points[5], &p)) + 0.01f);
}
const struct vec4f* gfx_csm_get_cascades(const struct mat3f* view)
{
static struct vec4f cascades[CSM_CASCADE_CNT];
struct vec4f center;
for (uint i = 0; i < CSM_CASCADE_CNT; i++) {
const struct sphere* s = &g_csm->cascades[i].bounds;
vec3_setf(¢er, s->x, s->y, s->z);
vec3_transformsrt(¢er, ¢er, view);
vec4_setf(&cascades[i], center.x, center.y, center.z, s->r);
}
return cascades;
}
struct sphere* sphere_xform(struct sphere* rs, const struct sphere* s, const struct mat3f* m)
{
/* we have to transform radius by scale value of transform matrix
* to determine scale value, we find the highest scale component of the matrix */
float xlen = m->m11*m->m11 + m->m12*m->m12 + m->m13*m->m13;
float ylen = m->m21*m->m21 + m->m22*m->m22 + m->m23*m->m23;
float zlen = m->m31*m->m31 + m->m32*m->m32 + m->m33*m->m33;
float isqr_scale = maxf(xlen, ylen);
isqr_scale = maxf(isqr_scale, zlen);
/* transform center */
struct vec4f c;
vec3_setf(&c, s->x, s->y, s->z);
vec3_transformsrt(&c, &c, m);
return sphere_setf(rs, c.x, c.y, c.z, s->r*sqrtf(isqr_scale));
}
void gfx_csm_prepare(const struct gfx_view_params* params, const struct vec3f* light_dir,
const struct aabb* world_bounds)
{
static const float tolerance = 10.0f;
struct vec3f dir;
vec3_setv(&dir, light_dir);
float texoffset_x = 0.5f + (0.5f/g_csm->shadowmap_size);
float texoffset_y = 0.5f + (0.5f/g_csm->shadowmap_size);
struct mat3f view_inv;
struct mat4f tex_mat;
struct mat4f tmp_mat;
float splits[CSM_CASCADE_CNT+1];
mat3_setf(&view_inv,
params->view.m11, params->view.m21, params->view.m31,
params->view.m12, params->view.m22, params->view.m32,
params->view.m13, params->view.m23, params->view.m33,
params->cam_pos.x, params->cam_pos.y, params->cam_pos.z);
mat4_setf(&tex_mat,
0.5f, 0.0f, 0.0f, 0.0f,
0.0f, -0.5f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
texoffset_x, texoffset_y, 0.0f, 1.0f);
float csm_far = minf(CSM_FAR_MAX, params->cam->ffar);
csm_split_range(params->cam->fnear, csm_far, splits);
/* calculate cascades */
struct frustum f; /* frustum points for cascades */
struct plane vp_planes[6];
for (uint i = 0; i < CSM_CASCADE_CNT; i++) {
cam_calc_frustumcorners(params->cam, (struct vec3f*)f.points, &splits[i], &splits[i+1]);
csm_calc_minsphere(&g_csm->cascades[i].bounds, &f, ¶ms->view, &view_inv);
memcpy(&g_csm->cascade_frusts[i], &f, sizeof(f));
/* cascade matrixes: first we find two extreme points of the world, related to cascade */
struct vec3f scenter;
struct ray r;
struct plane upper_plane;
struct plane lower_plane;
struct vec3f upper_pt;
struct vec3f lower_pt;
struct vec3f xaxis;
struct vec3f yaxis;
struct vec3f viewpos;
struct vec3f tmp;
struct vec3f lowerpt_vs;
float sr = g_csm->cascades[i].bounds.r;
vec3_setf(&scenter, g_csm->cascades[i].bounds.x, g_csm->cascades[i].bounds.y,
g_csm->cascades[i].bounds.z);
ray_setv(&r, &scenter, &dir);
plane_setv(&upper_plane, &g_vec3_unity_neg, fabs(world_bounds->maxpt.y));
plane_setv(&lower_plane, &g_vec3_unity, fabs(world_bounds->minpt.y));
vec3_sub(&upper_pt, &r.pt,
vec3_muls(&tmp, &dir, fabs(ray_intersect_plane(&r, &upper_plane)) + tolerance));
vec3_add(&lower_pt, &r.pt,
vec3_muls(&tmp, &dir, fabs(ray_intersect_plane(&r, &lower_plane)) + tolerance));
/* view matrix of light view for the cascade :
* dir = light_dir
* up = (1, 0, 0)
* pos = sphere center
*/
vec3_norm(&xaxis, vec3_cross(&tmp, &g_vec3_unitx, &dir));
vec3_cross(&yaxis, &dir, &xaxis);
vec3_sub(&viewpos, &upper_pt, vec3_muls(&tmp, &dir, tolerance));
mat3_setf(&g_csm->cascades[i].view,
xaxis.x, yaxis.x, dir.x,
xaxis.y, yaxis.y, dir.y,
xaxis.z, yaxis.z, dir.z,
-vec3_dot(&xaxis, &viewpos), -vec3_dot(&yaxis, &viewpos), -vec3_dot(&dir, &viewpos));
/* orthographic projection matrix for cascade */
vec3_transformsrt(&lowerpt_vs, &lower_pt, &g_csm->cascades[i].view);
float nnear = tolerance*0.5f;
float nfar = lowerpt_vs.z + sr;
csm_calc_orthoproj(&g_csm->cascades[i].proj,
sr*2.0f + 1.0f/g_csm->shadowmap_size,
sr*2.0f + 1.0f/g_csm->shadowmap_size,
nnear, nfar);
g_csm->cascades[i].nnear = nnear;
g_csm->cascades[i].nfar = nfar;
/* calculate final matrix */
mat3_mul4(&g_csm->cascade_vps[i], &g_csm->cascades[i].view, &g_csm->cascades[i].proj);
cam_calc_frustumplanes(vp_planes, &g_csm->cascade_vps[i]);
csm_calc_cascadeplanes(&g_csm->cascade_planes[i*4], vp_planes, &g_csm->cascade_vps[i]);
csm_round_mat(&g_csm->cascade_vps[i], &g_csm->cascade_vps[i], g_csm->shadowmap_size);
mat4_mul(&g_csm->shadow_mats[i],
mat3_mul4(&tmp_mat, &view_inv, &g_csm->cascade_vps[i]), &tex_mat);
}
/* caculate shadow area bounds (aabb) */
struct aabb cascade_near;
struct aabb cascade_far;
aabb_setzero(&g_csm->frustum_bounds);
aabb_from_sphere(&cascade_near, &g_csm->cascades[0].bounds);
aabb_from_sphere(&cascade_far, &g_csm->cascades[CSM_CASCADE_CNT-1].bounds);
aabb_merge(&g_csm->frustum_bounds, &cascade_near, &cascade_far);
vec3_setv(&g_csm->light_dir, &dir);
}
