OpenGL：从光源变形（缩放）模板阴影

Question

我的游戏引擎中有一个基本的模板阴影功能。我正在尝试根据我拥有的照明方向使阴影变形：

/*
 * @brief Applies translation, rotation and scale for the shadow of the specified
 * entity. In order to reuse the vertex arrays from the primary rendering
 * pass, the shadow origin must transformed into model-view space.
 */
static void R_RotateForMeshShadow_default(const r_entity_t *e) {
    vec3_t origin, delta;

    if (!e) {
        glPopMatrix();
        return;
    }

    R_TransformForEntity(e, e->lighting->shadow_origin, origin);

    VectorSubtract(e->lighting->shadow_origin, e->origin, delta);
    const vec_t scale = 1.0 + VectorLength(delta) / LIGHTING_MAX_SHADOW_DISTANCE;

    /*const vec_t dot = DotProduct(e->lighting->shadow_normal, e->lighting->dir);

    const vec_t sy = sin(Radians(e->angles[YAW]));
    const vec_t cy = cos(Radians(e->angles[YAW]));*/

    glPushMatrix();

    glTranslatef(origin[0], origin[1], origin[2] + 1.0);

    glRotatef(-e->angles[PITCH], 0.0, 1.0, 0.0);

    glScalef(scale, scale, 0.0);

}

我已经注释掉了地平面 (shadow_normal) 和光照方向的点积，以及模型偏航的 sin 和 cos，因为虽然我很确定它们是我需要增强的阴影的比例，我不知道产生透视正确变形的正确公式是什么。对于更了解预测的人来说，这可能是儿戏……对我来说，我是在黑暗中刺伤。

Answer 1

我最终能够通过管理我自己的矩阵和改编 SGI 的 OpenGL Cookbook 中的代码来达到预期的效果。该代码使用来自他的 DarkPlaces Quake 引擎的 LordHavoc 矩阵库。内联 cmets 列出了主要步骤。完整代码如下：

/*
 * @brief Projects the model view matrix for the given entity onto the shadow
 * plane. A perspective shear is then applied using the standard planar shadow
 * deformation from SGI's cookbook, adjusted for Quake's negative planes:
 *
 * ftp://ftp.sgi.com/opengl/contrib/blythe/advanced99/notes/node192.html
 */
static void R_RotateForMeshShadow_default(const r_entity_t *e, r_shadow_t *s) {
    vec4_t pos, normal;
    matrix4x4_t proj, shear;
    vec_t dot;

    if (!e) {
        glPopMatrix();
        return;
    }

    const cm_bsp_plane_t *p = &s->plane;

    // project the entity onto the shadow plane
    vec3_t vx, vy, vz, t;
    Matrix4x4_ToVectors(&e->matrix, vx, vy, vz, t);

    dot = DotProduct(vx, p->normal);
    VectorMA(vx, -dot, p->normal, vx);

    dot = DotProduct(vy, p->normal);
    VectorMA(vy, -dot, p->normal, vy);

    dot = DotProduct(vz, p->normal);
    VectorMA(vz, -dot, p->normal, vz);

    dot = DotProduct(t, p->normal) - p->dist;
    VectorMA(t, -dot, p->normal, t);

    Matrix4x4_FromVectors(&proj, vx, vy, vz, t);

    glPushMatrix();

    glMultMatrixf((GLfloat *) proj.m);

    // transform the light position and shadow plane into model space
    Matrix4x4_Transform(&e->inverse_matrix, s->illumination->light.origin, pos);
    pos[3] = 1.0;

    const vec_t *n = p->normal;
    Matrix4x4_TransformPositivePlane(&e->inverse_matrix, n[0], n[1], n[2], p->dist, normal);

    // calculate shearing, accounting for Quake's negative plane equation
    normal[3] = -normal[3];
    dot = DotProduct(pos, normal) + pos[3] * normal[3];

    shear.m[0][0] = dot - pos[0] * normal[0];
    shear.m[1][0] = 0.0 - pos[0] * normal[1];
    shear.m[2][0] = 0.0 - pos[0] * normal[2];
    shear.m[3][0] = 0.0 - pos[0] * normal[3];
    shear.m[0][1] = 0.0 - pos[1] * normal[0];
    shear.m[1][1] = dot - pos[1] * normal[1];
    shear.m[2][1] = 0.0 - pos[1] * normal[2];
    shear.m[3][1] = 0.0 - pos[1] * normal[3];
    shear.m[0][2] = 0.0 - pos[2] * normal[0];
    shear.m[1][2] = 0.0 - pos[2] * normal[1];
    shear.m[2][2] = dot - pos[2] * normal[2];
    shear.m[3][2] = 0.0 - pos[2] * normal[3];
    shear.m[0][3] = 0.0 - pos[3] * normal[0];
    shear.m[1][3] = 0.0 - pos[3] * normal[1];
    shear.m[2][3] = 0.0 - pos[3] * normal[2];
    shear.m[3][3] = dot - pos[3] * normal[3];

    glMultMatrixf((GLfloat *) shear.m);

    Matrix4x4_Copy(&s->matrix, &proj);
}

这里有完整的实现： https://github.com/jdolan/quake2world/blob/master/src/client/renderer/r_mesh_shadow.c